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What is an equation of the line that passes through the point (−3,−5) and is parallel to the line 2x+3y=15

 Nov 29, 2022
edited by Guest  Nov 29, 2022
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2x + 3y = 15 can be written as 3y = -2x + 15     =>    y = -2x/3 + 5

The slope of this line is -2/3, and if a line is parallel to it, it must also have a slope of -2/3. So the new line is y = -2x/3 + b, where b is the y-intercept.

Plug in (-3, -5): -5 = -2(-3)/3 + b, b = -7

Equation of line: y = -2x/3 - 7 or in standard form: 2x + 3y = -21

 

 

PS: smarter solution is to know that new line would be 2x + 3y = c, and plug in -3, -5 to obtain -21. That's if you know the rule about parallel lines + slopes.

 Nov 29, 2022

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