Question

5x-5y/4=4x-4/2 Find the equation of the line which passes through the point (10,7) and is perpendicular to the given line. Express in slope intercept form.

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

(5x-5y)/4= (4x-4)/2

Cross multiplying

2(5x - 5y) = 4(4x - 4)

10x - 10y = 16x - 16

10y = - 6x + 16

y = -6x/10 + 16/10

Comparing with the slope intercept form,

Slope, m = - 6/10

This means that the slope of the line that is perpendicular to it is 10/6

The given points are (10,7)

To determine c,

We will substitute m = 10/6, y = 7 and x = 10 into the equation, y = mx + c. It becomes

7 = 10/6 × 10 + c

7 = 100/6 + c

7 = 50/3 + c

c = 7 - 50/3

c = - 29/3

The equation becomes

y = 10x/6 - 29/3