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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=12x3(-1,2), y=\frac{1}{2} x-3

Solution

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y=mx+b2=12(1)+b2=12+b52=b\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=12x3y=\dfrac{1}{2}x-3 has a slope of 12\dfrac{1}{2}, then the slope of the line you must write has a slope of m=12m=\dfrac{1}{2}. Substitute this slope and the point (1,2)(-1,2) into slope-intercept form of a line and solve for bb.

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