The standard equation for a line with slope m and which passes through the point (x_0,y_0) is given by:
On the other hand, the standard equation for a line with slope m and y-intercept b is given by:
Comparing the last equation with y=-2x+7, we know that its slope m is equal to -2.
For two lines to be perpendicular, their slopes have to satisfy the condition that the product of their slopes is equal to -1. Therefore, a line perpendicular to y=-2x+7 has to have a slope of 1/2, so that (1/2)(-2)=-1.
Use m=1/2, x_0=4 and y_0=7 to find the line perpendicular to y=-2x+7 which goes through the point (4,7), by substituting those values in the point-slope equation:
