what is an equation in slope-intercept form for the line that passes through the points (1, -3) and (3, 1)?
To find the equation of the line that passes through the points (1, -3) and (3, 1), you can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-3)) / (3 - 1) = 4 / 2 = 2
Now that we have the slope (m), we can substitute it into the equation as follows:
y = 2x + b
To find the y-intercept (b), we can substitute the coordinates of one of the points into the equation. We'll use the point (1, -3):
-3 = 2(1) + b
-3 = 2 + b
b = -3 - 2
b = -5
Now we have the slope (m = 2) and the y-intercept (b = -5), so we can write the final equation in slope-intercept form:
y = 2x - 5