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#
