Question

Write an equation in slope-intercept form of the line that passes through (2,0) and is perpendicular to y=1/5 x-2.

Answer 1

`y = -5x+10`

Explanation:

Given

`(x_1,y_1) = (2,0)`

`y = (1)/(5)x - 2`

Required

Determine an equation that perpendicular to the equation

An equation has the form:

`y = mx + b`

Where

`m = slope`

By comparison:

`m = (1)/(5)`

Next, we determine the slope of the new line.

When two lines are perpendicular, the following relation exist:

`m_2= -(1)/(m_1)`

Substitute 1/5 for m1

`m_2= -(1)/(1/5)`

`m_2= -5`

The equation of the line is then calculated using:

`y - y_1 = m(x - x_1)`

Where:

`m_2= -5` and
`(x_1,y_1) = (2,0)`

This gives:

`y - 0 = -5(x - 2)`

`y = -5(x - 2)`

`y = -5x+10`