Question

Write the equation of a line that is parallel to the given line and passes through the given point.

y=1/3x+1 (-3,4)

Answer 1

`y=(1)/(3)x +5`

Explanation:

Linear equations are typically formatted 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 the line crosses the y-axis)

1) Determine the slope (m)

Parallel lines will always have the same slope. Therefore, this line will also have a slope of
`(1)/(3)`. Plug this into our equation:

`y=(1)/(3) x+b`

2) Determine the y-intercept (b)

To solve for the y-intercept (b), plug the given point (-3,4) into our equation and isolate b.

`4=(1)/(3)(-3)+b\\4=(-3)/(3)+b\\4=-1+b`

Add 1 to both sides

`4+1=-1+b+1\\5=b`

Therefore, the y-intercept is 5. Plug this back into our original equation with the slope:

`y=(1)/(3)x +5`

I hope this helps!