Learning Outcomes
- Graph a line given the slope and a point on the line
In this chapter, we graphed lines by plotting points, by using intercepts, and by recognizing horizontal and vertical lines.
Another method we can use to graph lines is the point-slope method. Sometimes, we will be given one point and the slope of the line, instead of its equation. When this happens, we use the definition of slope to draw the graph of the line.
example
Graph the line passing through the point [latex]\left(1,-1\right)[/latex] whose slope is [latex]m=\Large\frac{3}{4}[/latex].
Solution
Plot the given point, [latex]\left(1,-1\right)[/latex].
Use the slope formula [latex]m=\Large\frac{\text{rise}}{\text{run}}[/latex] to identify the rise and the run.
[latex]\begin{array}{}\\ \\ m=\frac{3}{4}\hfill \\ \frac{\text{rise}}{\text{run}}=\frac{3}{4}\hfill \\ \\ \\ \text{rise}=3\hfill \\ \text{run}=4\hfill \end{array}[/latex]
Starting at the point we plotted, count out the rise and run to mark the second point. We count [latex]3[/latex] units up and [latex]4[/latex] units right.
Then we connect the points with a line and draw arrows at the ends to show it continues.
We can check our line by starting at any point and counting up [latex]3[/latex] and to the right [latex]4[/latex]. We should get to another point on the line.
try it
Graph a line given a point and a slope
- Plot the given point.
- Use the slope formula to identify the rise and the run.
- Starting at the given point, count out the rise and run to mark the second point.
- Connect the points with a line.
example
Graph the line with [latex]y[/latex] -intercept [latex]\left(0,2\right)[/latex] and slope [latex]m=-\Large\frac{2}{3}[/latex]
try it
example
Graph the line passing through the point [latex]\left(-1,-3\right)[/latex] whose slope is [latex]m=4[/latex]
try it
In the following video we show another example of how to graph a line given a point on the line and the slope of the line.
