Question

find the equation of the line that is perpendicular to 5x + y = 7 that passes through the point (10 0).

Answer 1

Find the slope of 5x + y = 7:

5x + y = 7

y = -5x + 7

Matching y = -5x + 7 with the equation format: y = mx + c, we can see that m = -5

Slope = m = - 5

.

Find the slope of the perpendicular line:

A perpendicular line to 5x + 7 = 7 will have the reciprocal slope

Slope of the perpendicular line = m = 1/5

.

Find the y-intercept of the new line:

Given that it passes through (10, 0)

y = 1/5x + c

0 = 1/5 (10) + c

0 = 2 + c

c = -2

The y-intercept = c = - 2

.

Form the equation :

y = mx + c

y = 1/5 x - 2

.

Answer: The line is y = 1/5 x - 2