Question

Find an equation of the line through the given point and perpendicular to the given line

Y=2x-2 and (-3, 5)

Answer 1

Explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The equation of the given line is

y = 2x - 2

Comparing with the slope intercept form,

Slope, m = 2

This means that the slope of the line that is perpendicular to it is -1/2

The given points are (-3, 5)

To determine c,

We will substitute m = -1/2, y = 5 and x = - 3 into the equation, y = mx + c

It becomes

5 = -1/2 × - 3 + c

5 = - 3/2 + c

c = 5 + 3/2

c = 13/2

The equation becomes

y = -x/2 + 13/2