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 2
1 answer:
Answer: y = (2/3)x - 5
Step-by-step 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.
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