Question

what is an equation of the line that passes through the point (-2, -3) and is perpindicular to the line x+3y=24

Answer 1

The equation of the line that passes through the point (-2, -3) and is perpendicular to the line will be:

• 
  `y=3x+3`

Explanation:

Given the line

`x+3y=24`

The slope-intercept form

`y = mx+b`

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

Writing the line equation in the slope-intercept form

`x+3y=24`

`y=-(1)/(3)x+8`

Thus, the slope = m = -1/3

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -1/3

perpendicular slope = – 1/m

`=-(1)/(-(1)/(3))=3`

Using the point-slope of the line equation

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

substituting perpendicular slope = 3 and (x₁, y₁) = (-2, -3)

`y-\left(-3\right)=3\left(x-\left(-2\right)\right)`

`y+3=3\left(x+2\right)`

subtract 3 from both sides

`y+3-3=3\left(x+2\right)-3`

`y=3x+3`

Therefore, the equation of the line that passes through the point (-2, -3) and is perpendicular to the line will be:

• 
  `y=3x+3`