Unit 5, Lesson 4
Equations of Lines
Integrated Math 1
4.1
Warm-up
The slope of the line in the image is . Explain how you know this is true.
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The slope of the line in the image is . Explain how you know this is true.
the line in the image
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 .
The equation is now in point-slope form, or , where:
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.
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 .