Slope-intercept form of a linear function looks like this:
y = color(purple)(m)x + color(blue)(b) where
color(purple)(m) = "slope"
color(blue)(b) = y"-intercept"
Using the given points, we can find the slope of the line:
"slope" = color(purple)(m) = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)
(y_2 - y_1)/(x_2 - x_1) = ((-1)-(-9))/(3 - 1) = 8/2 = 4/1 = color(purple)(4)
Putting this into our equation, we get:
y = color(purple)(4)x + color(blue)(b)
To find b, we can use one of the given points and the equation:
Let's use (3, -1) and solve for color(blue)(b):
y = 4x + color(blue)(b)
color(red)(-1) = 4 (color(red)(3)) + color(blue)(b)
-1 = color(red)(12) + color(blue)(b)
-1 color(red)(- 12) = 12 color(red)(- 12) + color(blue)(b)
color(red)(-13) = color(blue)(b)
Putting this into our equation, we get:
y = 4x + (-13)
or
y = 4x - 13
