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What is an equation of the line that passes through the point ( − 3 , − 7 ) (−3,−7) and is parallel to the line 2 x − 3 y = 24 2x−3y=24?

User Jonnybot
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1 Answer

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Answer: y = (2/3)x - 5

Explanation:

Parallel equations have a slope identical to the reference equation. The reference is 2x - 3y = 24

Rewrite this in slope/intercept form of y = mx + b, where m is the slope and y the y-intercept6:

2x - 3y = 24

-3y = -2x + 24

y = (2/3)x -8

The slope of (2/3) will also be the slope of the parallel line, so we can write:

y = (2/3)x + b

No matter the value of b, a line with this slope will be parallel to y = (2/3)x -8.

But we want a parallel line that goes through point (-3,-7). We can adjust the value of b to shift the line until it intersects (-3,-7), Determine b by entering the point into the equation and solving for b:

y = (2/3)x + b

-7 = (2/3)*(-3) + b for point (-3,-7)

-7 = -2 + b

b = -5

The equation becomes y = (2/3)x - 5

See attachment.

What is an equation of the line that passes through the point ( − 3 , − 7 ) (−3,−7) and-example-1
User Tola Odejayi
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4.7k points