Question

Write the equation of the line in slope intercept form.Through (-4, 6) and perpendicular to y = 2x - 3.

Answer 1

Explanation:

A perpendicular line will have the reciprocal and opposite slope. The slope of the given line is 2, so the slope of the line we want is -1/2.

For now we have:

$y=-\frac{1}{2}x+b$

To find the y-intercept b we use the point. We have to replace x = -4 and y = 6 into the expression above and solve for b:

$\begin{gathered} 6=-\frac{1}{2}\cdot(-4)+b \\ 6=2+b \\ b=4 \end{gathered}$

Answer:

The equation of the line is:

$y=-\frac{1}{2}x+4$