First, we need to determine the slope. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(-9) - color(blue)(7))/(color(red)(1) - color(blue)(5))#
#m = (-16)/-4 = 4#
We can now use the point-slope formula to find an equation for the line.
The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the slope and the first point in the problem gives:
#(y - color(red)(7)) = color(blue)(4)(x - color(red)(5))#
Now, solve for #y# to put the equation in slope intercept form:
#y - color(red)(7) = (color(blue)(4) xx x) - (color(blue)(4) xx color(red)(5))#
#y - color(red)(7) = 4x - 20#
#y - color(red)(7) + 7 = 4x - 20 + 7#
#y - 0 = 4x - 13#
#y = 4x - 13#
