How to Find the Y Intercept

Step-by-Step Guide

1. 1

   Step 1: Write down the slope and point.

   The slope or "rise over run" is a single number that tells you how steep the line is.
   
   This type of problem also gives you the (x,y) coordinate of one point along the graph.
   
   Skip to the other methods below if you don't have both these pieces of information.
   
   Example 1:
   A straight line with slope 2 contains the point (3,4).
   
   Find the y-intercept of this line using the steps below.
2. 2

   Step 2: Learn the slope-intercept form of an equation.

   Any straight line can be written as an equation in the form y = mx + b.
   
   When the equation is in this form, the variable m is the slope, and b is the y-intercept. , Write the slope-intercept equation, but instead of m, use the slope of your line.
   
   Example 1 (cont.): y = mx + bm = slope = 2y = 2x + b , Any time you have the coordinates of a single point on your line, you can substitute those x and y coordinates for the x and y in your line equation.
   
   Do this for the equation you've been working on.
   
   Example 1 (cont.):
   The point (3,4) is on this line.
   
   At this point, x = 3 and y =
   4.Substitute these values into y = 2x +b:4 = 2(3) + 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 answer.
   
   Example 1 (cont.): 4 = 2(3) + b4 = 6 + b4
   - 6 = b-2 = bThe y-intercept of this line is
   -2. , The y-intercept is the point where the line intersects with the y-axis.
   
   Since the y-axis is located at x = 0, the x coordinate of the y-intercept is always
   0.
   
   Example 1 (cont.):
   The y-intercept is at y =
   -2, so the coordinate point is (0,
   -2).
3. 3

   Step 3: Substitute the slope in this equation.

4. 4

   Step 4: Replace x and y with the coordinates of the point.

5. 5

   Step 5: Solve for b.

6. 6

   Step 6: Write this as a coordinate point.

Detailed Guide

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