Section 3.2 : Lines
4. Write down the equation of the line that passes through the following two points. Give your answer in point-slope form and slope-intercept form.
\[\left( {8,2} \right),\,\,\,\left( {14, - 7} \right)\]Show All Steps Hide All Steps
Start SolutionWe’ll need the slope of the line in order to write down the equation 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.
\[m = \frac{{ - 7 - 2}}{{14 - 8}} = \frac{{ - 9}}{6} = \require{bbox} \bbox[2pt,border:1px solid black]{{ - \frac{3}{2}}}\] Show Step 2We’ll use the point-slope form to write down the equation of the line. This requires a single point and we can use either of the points from the problem statement.
Either will give an acceptable answer here. We’ll give both possible answers for the point-slope form.
\[\begin{align*} & \left( {14, - 7} \right)\,\,\,\,:\,\,\,\,\,\,\require{bbox} \bbox[2pt,border:1px solid black]{{y = - 7 - \frac{3}{2}\left( {x - 14} \right)}}\\ & \left( {8,2} \right)\,\,\,\,:\,\,\,\,\,\,\,\,\,\,\,\,\require{bbox} \bbox[2pt,border:1px solid black]{{y = 2 - \frac{3}{2}\left( {x - 8} \right)}}\end{align*}\] Show Step 3To get the answer in slope-intercept form all we need to do is take one of the answers from Step 2 and distribute the slope through the parenthesis and simplify. You will get the same answer regardless of which one you chose to use.
Doing this gives,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{y = - \frac{3}{2}x + 14}}\]