### Finding Slope from Two Points Worksheets

Free finding slope from two points worksheets in free response and multiple-choice modes for students and teachers. Finding slope from two points is one of the ways to find a slope of a given line.

Recall that the slope of a line is a measure of how the y–values change with respect to a change in their corresponding x–values.

Slope of a Line Given Two Points

Let $$\left(x_1,y_1 \right)$$ and $$\left(x_2,y_2 \right)$$ be two distinct points of a line, the vertical change is $$y_2-y_1$$ and the horizontal change is $$x_2-x_1$$. The slope, $$m$$ of the line is defined by the equation, $$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$$.

Examples

Find the slope of a line that passes through each given pair of points.

\small \begin{align*}\displaystyle &1.\;\;\; \left ( 2,-3 \right );\;\left ( 3,0 \right )\\&2.\;\;\; \left ( -1,2 \right );\;\left ( -2,4 \right )\\&3.\;\;\; \left ( \frac{1}{2},\frac{1}{4} \right );\;\left ( 2,4 \right )\\&4.\;\;\; \left ( 2,-2 \right );\;\left ( 0,3 \right )\\&5.\;\;\; \left ( 2,2 \right );\;\left ( 8,-3 \right )\\&6.\;\;\; \left ( 2,\frac{1}{2} \right );\;\left ( -1,5 \right ) \end{align*}

\small \begin{align*}\displaystyle &1.\;\;\; m=\frac{0-\left ( -3 \right )}{3-2}=\frac{3}{1}=3\\&2.\;\;\;m=\frac{4-2}{-2-\left ( -1 \right )}=\frac{2}{-1}=-2\\&3.\;\;\;m=\frac{4-\frac{1}{4}}{2-\frac{1}{2}}=\frac{3\frac{3}{4}}{1\frac{1}{2}}=\frac{\frac{17}{4}}{\frac{3}{2}}=\frac{17}{4}\times\frac{2}{3}=\frac{17}{6}\\&4.\;\;\;m=\frac{3-\left ( -2 \right )}{0-2}=\frac{5}{-2}=-\frac{5}{2}\\&5.\;\;\;\frac{-3-2}{8-2}=\frac{-5}{6}=-\frac{5}{6}\\&6.\;\;\;\frac{5-\frac{1}{2}}{-1-2}=\frac{\frac{9}{2}}{-3}=\frac{9}{2}\left (- \frac{1}{3} \right )=-\frac{9}{6}=-\frac{3}{2} \end{align*}