Mirabella G. answered • 12/19/13
Tutor
4.9
(122)
Passionate Tutor with Expertise in Math, Physics, and Test Prep
The definition of the slope of a line through points (x1, y1) and (x2, y2) is:
y2 - y1
x2 - x1
In the first case, this would be:
8 - 1 = 7
7 - (-11) 18
In the second case, this would be:
5 - (-2) = 7
11 - (-12) 23
The y-intercept of the aforementioned line must be found by first finding the equation for the line, using the slope-intercept form y = mx + b (where m is the slope and b is the y-intercept). We have already found the slope, so we can put this in as m. We have two choices of (x, y) pairs for each case, so we can plug one of these into the equation, leaving just one unknown, b. Solve for b, and you have the y-intercept. I will do this for the first case.
y = 7 x + b
18
8 = 7 (7) + b
18
8 = 49 + b
18
144 - 49 = b
18 18
b = 95
18
The method for the second case is exactly the same, just with different numbers. Now you know how to find slopes and intercepts, which means you know how to write the equation of a line through two points!
