Algebra - Lines

Section 3.2 : Lines

1. Determine the slope of the line containing the two points below and sketch the graph of the line.

\[\left( { - 2,4} \right),\,\,\,\left( {1,10} \right)\]

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Start Solution

Let’s find the slope of the line. We’ll let the first point listed above be the point $\left( {{x_1},{y_1}} \right)$ and the second point listed be the point $\left( {{x_2},{y_2}} \right)$ in the slope formula. Note that it doesn’t really matter which point is which. All that matters is that you stay consistent when you plug values into the formula.

Here’s the slope.

\[m = \frac{{10 - 4}}{{1 - \left( { - 2} \right)}} = \frac{6}{3} = 2\]

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Here is a sketch of the line.

$The graph of the line through the two given points. It is a straight line rising from left to right and the points $\left( { - 2,4} \right)$ and $\left( {1,10} \right)$ are marked and labeled on it, along with the extra point $\left( {0,8} \right)$. A small dashed right triangle is drawn between $\left( {0,8} \right)$ and $\left( {1,10} \right)$ with the horizontal side labeled Run = 1 and the vertical side labeled Rise = 2 to illustrate the slope.$

We’ve included an extra point, $\left( {0,8} \right)$, to help illustrate the slope we computed in Step 1.