What is an equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1)
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
Given points (1,-3) and (3,1), we can find the slope as (change in y) / (change in x):
m = (1 - (-3)) / (3 - 1)
= 4/2
= 2
So, the slope of the line is 2.
Now, we can plug in the slope and one of the points (1,-3) into the slope-intercept form to find the y-intercept, b:
-3 = 2(1) + b
-3 = 2 + b
b = -5
Thus, the equation in slope-intercept form for the line that passes through the points (1,-3) and (3,1) is:
y = 2x - 5.