First, we need to determine the slope of the line. 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)(1/2) - color(blue)(7))/(color(red)(0) - color(blue)(-5)) = (color(red)(1/2) - color(blue)(7))/(color(red)(0) + color(blue)(5)) = (color(red)(1/2) - (2/2 xx color(blue)(7)))/5 = #
#(color(red)(1/2) - 14/2)/5 = (-13/2)/5 = -13/10#
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 we calculated and the values from the first point in the problem gives:
#(y - color(red)(7)) = color(blue)(-13/10)(x - color(red)(-5))#
#(y - color(red)(7)) = color(blue)(-13/10)(x + color(red)(5))#
We can also substitute the slope we calculated and the values from the second point in the problem giving:
#(y - color(red)(1/2)) = color(blue)(-13/10)(x - color(red)(0))#
Or
#(y - color(red)(1/2)) = color(blue)(-13/10)x#
