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Write an equation in slope-intercept form for the line that is parallel to the line 6x + 2y = 2 and passes through the point

(-1, 7).

User Thaangaraj
by
8.1k points

1 Answer

5 votes

Answer:


y=-3x+4

Explanation:

Hi there!

What we need to know:

  • Slope-intercept form:
    y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
  • Parallel lines have the same slope (m) and different y-intercepts (b)

1) Determine the slope (m)


6x+2y=2

Rearrange this equation in slope-intercept form (so it's easier for us to identify the slope)

Subtract 6x from both sides to isolate 2y


6x+2y-6x=-6x+2\\2y=-6x+2

Divide both sides by 2 to isolate y


y=-3x+1

Now, we can tell clearly that -3 is in the place of m. Therefore, because parallel lines have the same slope, we know that the line we're solving for will also have a slope of -3. Plug this into
y=mx+b:


y=-3x+b

2) Determine the y-intercept


y=-3x+b

Plug in the given point (-1,7)


7=-3(-1)+b\\7=3+b

Subtract 3 from both sides


7-3=3+b-3\\4=b

Therefore, the y-intercept of the line is 4. Plug this back into
y=-3x+b:


y=-3x+4

I hope this helps!

User Su Zhang
by
7.2k points

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