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)(0) - color(blue)(-2))/(color(red)(7) - color(blue)(0)) = (color(red)(0) + color(blue)(2))/(color(red)(7) - color(blue)(0)) = 2/7#
The point-slope form of a linear equation is: #(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#
Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope.
Substituting the slope we calculated and the values from the first point in the problem gives:
#(y - color(blue)(-2)) = color(red)(2/7)(x - color(blue)(0))#
#(y + color(blue)(2)) = color(red)(2/7)(x - color(blue)(0))#
Or
#(y + color(blue)(2)) = color(red)(2/7)x#
We can also substitute the slope we calculated and the values from the second point in the problem giving:
#(y - color(blue)(0)) = color(red)(2/7)(x - color(blue)(7))#
Or
#y = color(red)(2/7)(x - color(blue)(7))#
