Question

What is the equation of the line that is parallel to the line whose equation is y=-4/3x+7/3 and also passes through the point (-5,2)

Answer 1

`y=-(4)/(3) x-(14)/(3)`

Explanation:

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)

1) Determine the slope (m)

Parallel lines will always have the same slope. Therefore, this line will have the same slope as the given line
`y=-(4)/(3) x+ (7)/(3)`.

Plug in
`-(4)/(3)` as the slope

`y=-(4)/(3) x+b`

2) Determine the y-intercept (b)

To find the y-intercept, plug the given point (-5,2) into the equation and solve for b.

`2=-(4)/(3)(-5)+b\\2=(20)/(3)+b`

Subtract both sides by
`(20)/(3)`

`2-(20)/(3) = (20)/(3)+b-(20)/(3)\\(6)/(3) -(20)/(3)=b\\-(14)/(3) = b`

Therefore, the y-intercept is
`-(14)/(3)`.

3) Plug the y-intercept back into our original equation

`y=-(4)/(3) x-(14)/(3)`

I hope this helps!