Question

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

Give your answer in the form y=mx+b.

Answer 1

y=4x−16

Explanation:

Because we want a parallel line to the given one, we know it needs to have the same slope. Therefore, the new line must be y=4x+b for some b. Knowing that the line goes through the point (6,8), we can plug this in and solve for b:

y=4x+b

8=4(6)=b

b=-16

So the equation of the line is y=4x−16.

Answer 2

`y=4x-16`

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!