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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).

Respuesta :

theleangreenbean

Answer:

[tex]y=-3x+4[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

  • Slope-intercept form: [tex]y=mx+b[/tex] 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)

[tex]6x+2y=2[/tex]

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

[tex]6x+2y-6x=-6x+2\\2y=-6x+2[/tex]

Divide both sides by 2 to isolate y

[tex]y=-3x+1[/tex]

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 [tex]y=mx+b[/tex]:

[tex]y=-3x+b[/tex]

2) Determine the y-intercept

[tex]y=-3x+b[/tex]

Plug in the given point (-1,7)

[tex]7=-3(-1)+b\\7=3+b[/tex]

Subtract 3 from both sides

[tex]7-3=3+b-3\\4=b[/tex]

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

[tex]y=-3x+4[/tex]

I hope this helps!

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