Question

Write the equation of the line which passes through (2, –3) and is perpendicular to y = 4x + 7 in standard form.

Answer 1

A perpendicular line will have a slope that is the opposite reciprocal of the current slope. So the slope of the new line will be -1/4.

Using the new slope and the point given, substitute into the point slope formula y=mx+b and solve for b
-3=-1/4(2)+b

Answer 2

b=7/2 so the equation is y=-1/4x+7/2

BUT--you said standard form, Ax+By=C
y=-1/4x+7/2 1/4x+y=7/2

multiply everything by 4 to eliminate the fraction
4(1/4x+y=7/2)
x+4y=14