1 Answer

Ducky · Answer 1 · 2021-10-27T18:35:48+0000

Answer:

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

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:

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