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Graphing a Line Given a Point and a Slope

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Graphing a Line Given a Point and a Slope

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Site gives you one question at a time, for another click on "Try another version of this question"

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Learning Objectives

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=\frac{3}{4}[/latex].

Solution
Plot the given point, [latex]\left(1,-1\right)[/latex].

Use the slope formula [latex]m=\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.

Graph a line given a point and a slope

1. Plot the given point.

2. Use the slope formula to identify the rise and the run.

3. Starting at the given point, count out the rise and run to mark the second point.

4. 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=-\frac{2}{3}[/latex].

example

Graph the line passing through the point [latex]\left(-1,-3\right)[/latex] whose slope is [latex]m=4[/latex].

Solve Slope Applications

At the beginning of this section, we said there are many applications of slope in the real world. Let's look at a few now.

example

The pitch of a building's roof is the slope of the roof. Knowing the pitch is important in climates where there is heavy snowfall. If the roof is too flat, the weight of the snow may cause it to collapse. What is the slope of the roof shown?

example

Have you ever thought about the sewage pipes going from your house to the street? Their slope is an important factor in how they take waste away from your house.

Sewage pipes must slope down [latex]\frac{1}{4}[/latex] inch per foot in order to drain properly. What is the required slope?

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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.

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Quick Check: Find Slope Given Two Points

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Quick Check: Find Slope Given Two Points

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Slope from two points | Algebra (practice) | Khan Academy

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Finding Slope of a Line from an Equation

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Finding Slope of a Line from an Equation

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grade 8  free math games practice common core standards

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Quick Check: Writing Equations in Slope Intercept Form Given a Word Problem

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Quick Check: Writing Equations in Slope Intercept Form Given a Word Problem

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Slope-intercept form word problems - Quiz

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Preview this quiz on Quizizz. In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.

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Quick Check: Finding Equations Given a Point and Slope & Finding Equations Given 2 Points

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Quick Check: Finding Equations Given a Point and Slope & Finding Equations Given 2 Points

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Quick Check: Writing Equations Given Two Points or a Point and Slope

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Quick Check: Writing Equations Given Two Points or a Point and Slope

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two points and point slope word problems

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Quick Check: Standard Form to Slope-Intercept Form

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Quick Check: Standard Form to Slope-Intercept Form