Question

Find the equation of the line that is parallel to y = 4 - 3x and passes through the

point (1,5).

Answer 1

`y=-3x+8`

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

1) Determine the slope (m)

`y = 4 - 3x\\y = -3x+4`

Given this equation, we can identify the slope to be -3 since it's in the place of m in
`y=mx+b`.

Because parallel lines have the same slope, -3 is therefore the slope of the line we're currently solving for. Plug this into
`y=mx+b`:

`y=-3x+b`

2) Determine the y-intercept (b)

`y=-3x+b`

Plug in the given point (1,5) and solve for b:

`5=-3(1)+b\\5=-3+b\\8=b`

Therefore, the y-intercept is 8. Plug this back into
`y=-3x+b`:

`y=-3x+8`

I hope this helps!