How do you write an equation in slope-intercept form for the line that passes through (4,-2) and is parallel to the graph of y=1/2x-7?

Nov 19, 2016

$y = \frac{1}{2} x - 4$

Explanation:

Equation of line through $\left(4 , - 2\right)$ and parallel to $y = \frac{1}{2} x - 7$

The given equation is in the form $y = m x + b$, where $m =$slope.

Parallel lines have equal slopes, so the slope of the line we are trying to find is $m = \frac{1}{2}$.

Next, use the point-slope form of a line:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $\left({x}_{1} , {y}_{1}\right)$ is a point on the line.

$y - - 2 = \frac{1}{2} \left(x - 4\right)$

$y + 2 = \frac{1}{2} x - 2$
$\textcolor{w h i t e}{a} - 2 \textcolor{w h i t e}{a a a a a a} - 2$

$y = \frac{1}{2} x - 4$

OR

Use the slope intercept form of a line (again with $m = \frac{1}{2}$):

$y = m x + b$ where $b =$the $y$ intercept.

Plug in $\left(4 , - 2\right)$ for $x \mathmr{and} y$ and solve for $b$.

$- 2 = \frac{1}{2} \left(4\right) + b$

$- 2 = \textcolor{w h i t e}{a {a}^{2}} 2 + b$
$- 2 = - 2$

$- 4 = b$

The equation is then $y = \frac{1}{2} x - 4$