Question

what is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3

Answer 1

A perpendicular line will have a negative reciprocal slope (-1/2 → 2/1)
Use the given point to find the y-intercept "b" in y = mx+b

y = 2x + b
2 = 2(-7) + b
2 = -14 + b
2 + 14 = b
16 = b

final equation :
y = 2x + 16

Answer 2

first off, what is the slope of say y = -1/2x+3? well, let's take a peek


`\bf y=\stackrel{slope}{-\cfrac{1}{2}}x+3`

well, then, a line perpendicular to that line, will have a slope that is negative reciprocal to that one, so if the slope of that graph is -1/2, then


`\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{2}\\\\ slope=-\cfrac{1}{{{ 2}}}\qquad negative\implies +\cfrac{1}{{{ 2}}}\qquad reciprocal\implies + \cfrac{{{ 2}}}{1}\implies 2`

so, we're really looking for the equation of a line whose slope is 2, and runs through -7, 2.