Question

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

Answer 1

Answer:

$y=-3x+4$

Step-by-step 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!