Question

write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the given line.(5,-1); y=4x -7 (4,-2); y=3

Answer 1

The given line is

$y=4x-7$

Since the equation is in slope-intercept form, we can deduct that its slope is m = 4.

It is important to know that a perpendicular line would have an opposite and reciprocal slope, which is -1/4, that's the slope of the new perpendicular line.

Then, we use the point-slope formula

$\begin{gathered} y-y_1=m(x-x_1) \\ \end{gathered}$

Where,

$\begin{gathered} x_1=5_{} \\ y_1=-1 \end{gathered}$$\begin{gathered} y-(-1)=-\frac{1}{4}(x-5) \\ y+1=-\frac{1}{4}x+\frac{5}{4} \\ y=-\frac{1}{4}x+\frac{5}{4}-1 \\ y=-\frac{1}{4}x+\frac{5-4}{4} \\ y=-\frac{1}{4}x+\frac{1}{4} \end{gathered}$

Hence, the answer is y = -1/4x + 1/4.

On the other hand, the equation y = 3 refers to a horizontal line that passes through (0,3).

A perpendicular line that passes through (4, -2) would be x = 4 because it would represent a vertical line that passes through that point.

Hence, the answer is x = 4.