Question

What is an equation of the line that passes through the point (-6,-8) and is parallel to the line x-2y=6?

Answer 1

Answer:

$y=\frac{1}{2}x-5$

Step-by-step 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 the line crosses the y-axis)
• Parallel lines always have the same slope and different y-intercepts

1) Determine the slope (m)

$x-2y=6$

Rearrange this equation into slope-intercept form (this will help us find the slope)

Subtract x from both sides

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

Divide both sides by -2

$y=\frac{1}{2} x-3$

Now, we can identify clearly that the slope of the given line is $\frac{1}{2}$ since it's in the place of m. Because parallel lines always have the same slopes, the line we're currently solving for would therefore have a slope of $\frac{1}{2}$ as well. Plug this into $y=mx+b$:

$y=\frac{1}{2}x+b$

2) Determine the y-intercept (b)

$y=\frac{1}{2}x+b$

Plug in the given point (-6,-8)

$-8=\frac{1}{2}(-6)+b\\-8=-3+b$

Add 3 to both sides to isolate b

$-8+3=-3+b+3\\-5=b$

Therefore, the y-intercept is -5. Plug this back into $y=\frac{1}{2}x+b$:

$y=\frac{1}{2}x-5$

I hope this helps!