Passing through (2, 2) and perpendicular to the line whose equation is y = 4x + 7; point-slope form

Question

Use the given conditions to write an equation for the line
in the indicated form.

Answer 1

For a line to be perpendicular the slope must be a negative reciprocal of the other line slope>

 

Since the equation y = 4*x + 7  has a slope = 4, the negative reciprocal of this slope is -1/4

 

Therefore, passing through points (2,2) or x0 = 2 and y0 = 2, fill in values for new perpendicular equation

 

y - y0  = (x - x0)*m

 

y  = (x - x0)*m  + y0

 

y  =  (x - 2)*(-1/4)  + 2

 

y  * (-1/4)*x + 1/2 + 2

 

y = (-1/4)*x + 5/2       Equation of line that is perpendicular and passes through (2,2)