Question

Write the equation of the line passing through points (-1,0) and perpendicular to the line y=1/3x-7

Answer 1

Using the point-slope form of the equation, the equation of the line passing through (-1,0) and perpendicular to the line is:

`y=-3x-3`

Explanation:

We know the slope-intercept of line equation is

`y=mx+b`

where m is the slope, and b is the y-intercept

Given the line

`y=\:(1)/(3)x-7`

Thus, the slope of the line is:

m=1/3

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be: -3

Therefore, using the point-slope form of the equation, the equation of the line passing through (-1,0) and perpendicular to the line is:

`y-y_1=m\left(x-x_1\right)`

`y-0=-3\left(x-\left(-1\right)\right)`

`y=-3\left(x+1\right)`

`y=-3x-3`