Question

Which equation represents a line that passes through the point (10, 7) and is perpendicular to the graph of the equation y = 5x − 4?

Answer 1

The answer is : y = -0.2x + 9



The gradient of the perpendicular line is -0.2

y = -0.2x + c

To find c, you have to substitute the x and y values, which are from the point given (10,7)

7 = -0.2(10) +c

7 + 2 = c

c = 9

y = -0.2x + 9

Answer 2

y = -
`(1)/(5)` x + 9

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x - 4 ← is in slope- intercept form

with slope m = 5

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(5)` , then

y = -
`(1)/(5)` x + c ← is the partial equation

to find c substitute (10, 7 ) into the partial equation

7 = -
`(1)/(5)` (10) + c = - 2 + c ( add 2 to both sides )

9 = c

y = -
`(1)/(5)` x + 9 ← equation of perpendicular line