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Unit 5, Lesson 4

Equations of Lines

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Integrated Math 1

4.1

Warm-up

Remembering Slope

<p>Line. Points plotted at -10 comma -6 and 5 comma 2.</p>

The slope of the line in the image is . Explain how you know this is true.

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4.2

Activity

Building an Equation for a Line

Standards Alignment

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The image shows a line.
1. Write an equation that says the slope between the points and is 2.
2. Look at this equation:
  How does it relate to the equation you wrote?
Here is an equation for another line:
1. What point do you know this line passes through?
2. What is the slope of this line?
Next, let’s write a general equation that we can use for any line. Suppose we know that a line passes through a particular point, .
1. Write an equation that says the slope between points and is .
2. Look at this equation: . How does it relate to the equation you wrote?

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4.3

Activity

Using Point-Slope Form

Standards Alignment

Building On

Addressing

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Write an equation that describes each line.
1. the line passing through point with slope
2. the line passing through point with slope
3. the line passing through point with slope -1
4. the line in the image
Using the structure of the equation, what point do you know each line passes through? What’s the line’s slope?

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Student Lesson Summary

The line in the image can be defined as the set of points that have a slope of 2 with the point .

An equation that says point has slope 2 with is . This equation can be rearranged to look like .

<p>Line, y intercept = -2., slope of 2. Points plotted at 3 comma 4 and x comma y.</p>

The equation is now in point-slope form, or , where:

is any point on the line.
is a particular point on the line that we choose to substitute into the equation.
is the slope of the line.

Other ways to write the equation of a line include slope-intercept form, , and standard form, .

To write the equation of a line passing through and , start by finding the slope of the line. The slope is because . Substitute this value for to get . Now we can choose any point on the line to substitute for . If we choose , we can write the equation of the line as .

We could also use as the point, giving . We can rearrange the equation to see how point-slope and slope-intercept forms relate, getting . Notice that is the -intercept of the line. The graphs of all three of these equations look the same.

Glossary

point-slope form

Point-slope form is one way to write the equation of a line using its slope and the coordinates of one point on the line.

For a line with slope through the point , point-slope form is usually written as . It can also be written as .

<p>A line with point h comma k on an x y axis.</p>

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Lesson 4

Equations of Lines

Warm-up

Remembering Slope

Are You Ready for More?

Activity

Building an Equation for a Line

Standards Alignment

Building On

Addressing

A-SSE.1.a

Building Toward

G-GPE.5

Are You Ready for More?

Activity

Using Point-Slope Form

Standards Alignment

Building On

Addressing

A-SSE.A

Building Toward

G-GPE.5

Are You Ready for More?

Student Lesson Summary

Glossary

point-slope form

Have feedback on the curriculum?

Standards Alignment

Building On

8.EE.6

Addressing

Building Toward

G-GPE.5