Question

What is the equation of the line that contains the points with (x,y) coordinates (–3,7) and (5,–1) ?

Answer 1

(-3,7), (5,-1)

Slope-intercept form of the equation is,
y = mx + b
m = slope
b = y-intercept

To find slope, m
Slope m = (y2 - y1)/(x2 - x1)
m = (-1 - 7)/(5 - (-3))
m = -8/8 = -1

To find y-intercept, b
Use either point, (-3,7) and substitute the x and y values in the slope-intercept equation and solve for b.

y = mx + b, with m = -1
y = -1x + b
Point (-3,7)
7 = -1(-3) + b
7 = 3 + b
b = 4

So, your equation is,
y = -1x + 4
y = -x + 4