Example 1: A straight line with slope 2 contains the point (-3,4). Find the y-intercept of this line using the steps below.
Example 1 (cont. ): y = mx + bm = slope = 2y = 2x + b
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
Example 1 (cont. ): 4 = 2(3) + b4 = 6 + b4 - 6 = b-2 = bThe y-intercept of this line is -2.
Example 1 (cont. ): The y-intercept is at y = -2, so the coordinate point is (0, -2).
Example 2: A straight line passes through points (-1, 2) and (3, -4). Find the y-intercept of this line using the steps below.
“Rise” is the change in vertical distance, or the difference between the y-values of the two points. “Run” is the change in horizontal distance, or the difference between x-values of the same two points. Example 2 (cont. ): The y-values of the two points are 2 and -4, so the rise is (-4) - (2) = -6. The x-values of the two points (in the same order) are 1 and 3, so the run is 3 - 1 = 2.
Example 2 (cont. ): slope=riserun=−62={\displaystyle slope={\frac {rise}{run}}={\frac {-6}{2}}=} -3.
Example 2 (cont. ): y = mx + bSlope = m = -3, so y = -3x + bThe line includes a point with (x,y) coordinates (1,2), so 2 = -3(1) + b.
Example 2 (cont. ): 2 = -3(1) + b2 = -3 + b5 = bThe y-intercept is at (0,5).
Example 3: What is the y-intercept of the line x + 4y = 16? Note: Example 3 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 2).
Example 3 (cont. ): x + 4y = 16x = 00 + 4y = 164y = 16
Example 3 (cont. ): 4y = 164y4=164{\displaystyle {\frac {4y}{4}}={\frac {16}{4}}}y = 4. The y-intercept of the line is 4.
Example 4: To find the y-intercept of y2=x+1{\displaystyle y^{2}=x+1}, substitute x = 0 and solve the quadratic equation. In this case, we can solve y2=0+1{\displaystyle y^{2}=0+1} by taking the square root of both sides. Remember, when taking a square root, you must account for two answers: a negative and a positive. y2=1{\displaystyle {\sqrt {y^{2}}}={\sqrt {1}}}y = 1 or y = -1. These are both y-intercepts of this curve.
