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What is the equation of the line that is parallel to Y =-2/3 X +4 and that passes through (-2,-2)?

User Twifty
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1 Answer

4 votes

Answer:


y=-(2)/(3)x-(10)/(3)

Explanation:

Hi there!

What we need to know:

  • Linear equations are typically organized in slope-intercept form:
    y=mx+b where m is the slope and b is the y-intercept (the value of y when x is 0)
  • Parallel lines always have the same slope

1) Determine the slope (m)


y =-(2)/(3) x +4

In the given equation,
-(2)/(3) is in the place of m, making it the slope. Because parallel lines always have the same slope, the slope of the line we're currently solving for is
-(2)/(3). Plug this into
y=mx+b:


y=-(2)/(3)x+b

2) Determine the y-intercept (b)


y=-(2)/(3)x+b

Plug in the given point (-2,-2) to solve for b


-2=-(2)/(3)(-2)+b\\-2=(4)/(3)+b

Subtract
(4)/(3) from both sides to isolate b


-2-(4)/(3)=(4)/(3)+b-(4)/(3)\\-(10)/(3) =b

Therefore, the y-intercept of the line is
-(10)/(3). Plug this back into
y=-(2)/(3)x+b:


y=-(2)/(3)x-(10)/(3)

I hope this helps!

User Omid Nikrah
by
8.4k points

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