Question

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given line.

$(-1,2), y=\frac{1}{2} x-3$

Solution

VerifiedStep 1

1 of 3$\begin{align*} y&=mx+b\\ 2&=\dfrac{1}{2}(-1)+b\\ 2&=-\dfrac{1}{2}+b\\ \dfrac{5}{2}&=b \end{align*}$

Parallel lines have the same slope. Since $y=\dfrac{1}{2}x-3$ has a slope of $\dfrac{1}{2}$, then the slope of the line you must write has a slope of $m=\dfrac{1}{2}$. Substitute this slope and the point $(-1,2)$ into slope-intercept form of a line and solve for $b$.

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