Question

Find the equation of the line through (6,8) which is parallel to the line y=4x−6.

Answer 1

Answer:

$y=4x-16$

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 of the line 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)

$y=4x-6$

4 is in the place of m, making it the slope. Because parallel lines have the same slope, the slope of the line is therefore 4. Plug this into $y=mx+b$:

$y=4x+b$

2) Determine the y-intercept (b)

$y=4x+b$

Plug in the given point (6,8) and solve for b

$8=4(6)+b\\8=24+b$

Subtract 24 from both sides to isolate b

$8-24=24+b-24\\-16=b$

Therefore, the y-intercept of the line is -16. Plug this back into $y=4x+b$:

$y=4x-16$

I hope this helps!