how to find the y intercept of a graph

Download Commodity

Download Article

On their own, y-intercepts aren't complicated at all—they're merely points where the graph of the equation intersects with the Y-axis.^[1] But how are you supposed to find a y-intercept when you but have a limited corporeality of info on hand? Thankfully, it's not nearly every bit difficult as it looks. We'll walk yous through all the major ways to find the y-intercept when you already have the slope and a point, ii points, or just want to use a simple equation. With a footling practice, you can make quick work of any y-intercept problem that comes your way.

1
Write down the slope and point. ^[two] The slope or "rise over run" is a single number that tells you lot how steep the line is. This type of trouble also gives yous the (x,y) coordinate of i point along the graph. Skip to the other methods below if y'all don't have both these pieces of information.
- Instance 1: A straight line with slope 2 contains the point (-three,4). Find the y-intercept of this line using the steps beneath.
2

Learn the slope-intercept form of an equation. Any directly line can exist written as an equation in the form y = mx + b. When the equation is in this form, the variable chiliad is the gradient, and b is the y-intercept.

Ad
3
Substitute the slope in this equation. Write the slope-intercept equation, but instead of m, use the gradient of your line.
- Example one (cont.): y = mten + b
  thou = gradient = 2
  y = 2x + b
4
Supercede x and y with the coordinates of the betoken. Any time you have the coordinates of a single indicate on your line, you lot can substitute those x and y coordinates for the ten and y in your line equation. Practise this for the equation you've been working on.
- Example 1 (cont.): The bespeak (3,4) is on this line. At this point, 10 = 3 and y = 4.
  Substitute these values into y = iix +b:
  4 = 2(3) + b
5
Solve for b. Remember, b is the y-intercept of the line. Now that b is the only variable in the equation, rearrange to solve for this variable and find the reply.
- Example 1 (cont.): iv = 2(3) + b
  iv = 6 + b
  4 - 6 = b
  -two = b
  The y-intercept of this line is -2.
vi
Write this every bit a coordinate bespeak. The y-intercept is the point where the line intersects with the y-centrality. Since the y-axis is located at x = 0, the x coordinate of the y-intercept is ever 0.
- Example 1 (cont.): The y-intercept is at y = -2, then the coordinate point is (0, -ii).
Advertisement

1
Write down the coordinates of both points. ^[3] This method covers problems that only tell you 2 points on a direct line.^[four] Write each point coordinate downwards in (x,y) form.
- Case 2: A direct line passes through points (-1, 2) and (3, -four). Find the y-intercept of this line using the steps below.
2
Summate the rise and run. Slope is a mensurate of how much vertical distance the line moves for each unit of measurement of horizontal distance. You may accept heard this described as "rise over run" ( ${\frac {rise}{run}}$ ).^[5] Here's how to find these two quantities from two points:
- "Rise" is the modify in vertical distance, or the departure between the y-values of the two points.
- "Run" is the change in horizontal distance, or the divergence betwixt ten-values of the aforementioned two points.
- Instance ii (cont.): The y-values of the two points are 2 and -4, so the rising is (-4) - (two) = -vi.
  The ten-values of the two points (in the aforementioned order) are 1 and 3, so the run is iii - i = 2.
3
Split rising by run to find the slope. Now that y'all know these two values, plug them into " ${\frac {ascension}{run}}$ " to find the gradient of the line.
- Instance 2 (cont.): $slope={\frac {rise}{run}}={\frac {-6}{two}}=$ -three.
four

Review the slope-intercept form. You can depict a direct line with the formula y = mx + b, where thou is the slope and b is the y-intercept.^[6] Now that we know the gradient m and a point (ten,y), we can use this equation to solve for b, the y-intercept.
5
Fit the slope and point into the equation. Take the equation in gradient-intercept form and supervene upon chiliad with the slope you calculated. Supersede the x and y terms with the coordinates of a unmarried point on the line.^[7] It doesn't matter which bespeak y'all use.
- Instance ii (cont.): y = mx + b
  Slope = thousand = -3, so y = -3x + b
  The line includes a point with (x,y) coordinates (i,two), so 2 = -three(1) + b.
vi
Solve for b. Now the only variable left in the equation is b, the y-intercept. Rearrange the equation and then b is on 1 side, and y'all have your answer.^[eight] Remember, the y-intercept always has an 10-coordinate of 0.
- Example 2 (cont.): 2 = -3(1) + b
  ii = -iii + b
  5 = b
  The y-intercept is at (0,v).
Advertisement

1
Write down the equation of the line. If you already have the equation of the line, you can observe the y-intercept with a little algebra.^[9]
- Example three: What is the y-intercept of the line x + 4y = sixteen?
- Note: Instance three is a straight line. See the end of this section for an example of a quadratic equation (with a variable raised to the power of two).
2
Substitute 0 for x. The y-axis is a vertical line forth x = 0. This ways whatever point on the y-axis has an x-coordinate of 0, including the y-intercept of the line. Plug in 0 for x in the line equation.
- Instance 3 (cont.): x + 4y = 16
  x = 0
  0 + 4y = sixteen
  4y = 16
three
Solve for y. The answer is the y-intercept of the line.
- Example 3 (cont.): 4y = 16
  ${\frac {4y}{4}}={\frac {16}{four}}$
  y = iv.
  The y-intercept of the line is 4.
4

Confirm by graphing (optional) . To cheque your reply, graph the equation as neatly as yous tin can. The betoken where the line crosses the y-centrality is the y-intercept.
5

Discover the y-intercept for a quadratic equation. A quadratic equation includes a variable (x or y) raised to the ability of two. Yous tin solve for y with the same exchange, just since the quadratic describes a curve, information technology could intercept the y-axis at 0, 1, or two points. This means y'all may terminate up with 0, 1, or 2 answers.

Advertisement

Add together New Question

Question

How do you notice the ten-intercept in y = mx + b?

David Jia is an Bookish Tutor and the Founder of LA Math Tutoring, a private tutoring visitor based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well equally higher admissions counseling and test preparation for the Saturday, Human activity, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the Saturday, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor's degree in Concern Assistants. Additionally, David has worked every bit an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Large Ideas Math.

Academic Tutor

Expert Answer

Find the x-intercept by plugging in 0 for the value of y. The x-intercept will equal whatever value comes out at the other end of the equation.
Question

What do y'all hateful by x-intercept in math?

David Jia is an Bookish Tutor and the Founder of LA Math Tutoring, a individual tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well equally college admissions counseling and exam grooming for the Sabbatum, Deed, ISEE, and more than. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor's degree in Business concern Administration. Additionally, David has worked as an instructor for online videos for textbook companies such every bit Larson Texts, Big Ideas Learning, and Big Ideas Math.

Academic Tutor

Practiced Answer

The x-intercept is only wherever the graph crosses the x-centrality (the straight, horizontal line that cuts through the middle of the graph).
Question

If I have (3, -12) as my points and an x-intercept of i, what would the y-intercept be?

Solve by using Method ii above. You need 2 points to use that method. One signal is given as (iii,-12). The 2nd point is the given x-intercept, which is (i,0).
Question

If I am only given one specific point, how tin I convert it into slope intercept course?

Technist

Community Answer

You lot tin can't take only i point. Imagine you lot're standing in the eye of your neighborhood street and have no where to become. No direction, no distance, etc. You don't need to become to your friend's house or to schoolhouse. That is an instance of having only 1 point without whatsoever other point to go to so at that place'due south no line. Thus, no equation. And more chiefly, no math to work out.
Question

I do not become the terminal part of method ii, can you explain?

Using the "slope-intercept" form of the line'southward equation (y = mx + b), you solve for b (which is the y-intercept you're looking for). Substitute the known slope for one thousand, and substitute the known betoken'due south coordinates for x and y, respectively, in the slope-intercept equation. That will let you detect b. In the example in Method 2, the calculated slope is -3, then m becomes -3. The known bespeak is given as (1,two), so x in the equation becomes 1, and y becomes two. Thus, the slope-intercept equation becomes two = -3(1) + b. So 2 = -3 + b, and b = 5. That'southward the y-intercept.
Question

What do I do if the simply thing on the other side of the = is a variable?

If yous mean that the only thing on the "ten" side of the equation is x (so that y = ten), that indicates a slope (m) of ane and a y-intercept (b) of zilch.
Question

How exercise I find the y intercept when it is non numbered and manifestly a decimal?

Assuming past numbered you mean whole number, information technology doesn't matter, the method is the aforementioned in both cases.
Question

How do I find the y-intercept if 3x - y = six?

The graph crosses the y-axis when x=0, then substitute 0 for x in this equation, and solve for y: y is -6. Since y is -half dozen when 10 is 0, the y-intercept is -6.
Question

How do I observe the y-intercept if the only given information is the slope and no graph or point(due south) specified?

You would accept to be given more data than simply the slope in society to find the y-intercept.
Question

How do I find the slope for this and and so the y-intercept (0,0) and (4,-3)?

The gradient has a numerator consisting of the divergence betwixt any two ten values on the line and a denominator consisting of the departure betwixt the two corresponding y values. In this instance the slope is (4 - 0) / (-iii - 0), or 4 / -3, which equals -iv/three. The y-intercept is the y-value when ten=0. In this case, we are told that the line passes through the point (0,0), which means that the y-intercept is nil.

Show more than answers

Inquire a Question

200 characters left

Include your email accost to get a message when this question is answered.

Submit

Advertising

Video

For more than complicated equations, effort to isolate the terms containing y onto i side of the equation.
Some countries utilize a c or some other variable instead of b in the equation y = mx + b.^[10] This doesn't modify the meaning; it's merely a dissimilar tradition.
When calculating slope between ii points, you can subtract the x and y coordinates from each other in either order, as long every bit y'all put the points in the same gild for both rise and run.^[11] For example, the slope between (i, 12) and (iii, seven) tin be calculated in two dissimilar ways:

About This Article

Commodity Summary X

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y. If the equation is written in the slope-intercept form, plug in the gradient and the x and y coordinates for a bespeak on the line to solve for y. If you don't know the gradient, calculate it by dividing the ascent of the line past the run. If you want to observe the y-intercept if you simply know 2 points along the line, keep reading the article!

Did this summary assist you?

Cheers to all authors for creating a page that has been read 1,044,755 times.