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

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

Step-by-step explanation:

Given the line

The slope-intercept form

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

Writing the line equation in the slope-intercept form

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

Using the point-slope of the line equation

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

subtract 3 from both sides

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

step-by-step explanation: