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

Answer:

$y=-\frac{4}{3} x-\frac{14}{3}$

Step-by-step 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 $y=-\frac{4}{3} x+ \frac{7}{3}$.

Plug in $-\frac{4}{3}$ as the slope

$y=-\frac{4}{3} x+b$

2) Determine the y-intercept (b)

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

$2=-\frac{4}{3}(-5)+b\\2=\frac{20}{3}+b$

Subtract both sides by $\frac{20}{3}$

$2-\frac{20}{3} = \frac{20}{3}+b-\frac{20}{3}\\\frac{6}{3} -\frac{20}{3}=b\\-\frac{14}{3} = b$

Therefore, the y-intercept is $-\frac{14}{3}$.

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

$y=-\frac{4}{3} x-\frac{14}{3}$

I hope this helps!