Question

Which of the following lines would be perpendicular to a line whose equation is y=1/2x-7 and pass through the point (-10,7)?

Answer 1

Answer:

The answer to your question is     y = -2x - 13

Step-by-step explanation:

Data

Original line    y = 1/2x - 7

Point = (-10, 7)

New line = ?

Process

1.- Find the slope of the original line

    The slope is the coefficient of the x

                     y = 1/2x - 7

    slope = 1/2

2.- Find the slope of the new line

The new line is perpendicular to the original line

    slope = -2

3.- Find the equation of the new line

          y - y1 = m(x - x1)

          y - 7 = -2(x + 10)

-Simplification

          y - 7 = -2x - 20

          y = -2x - 20 + 7

          y = -2x - 13

Answer 2

Answer: The equation is y = -2x - 13.

We compare the given line with y = mx + b.

So slope = m = $\frac{1}{2}$.

We know that the slope of the perpendicular line is negative reciprocal.

It means the slope of the required line will be -2.

Given point = (-10, 7).

So, using the point slope formula the equation of the line is:

$y-7=-2(x+10)\\y-7=-2x-20\\y=-2x-13$

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