Objective 1 - Construct a linear function from points

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Use points to construct a linear function.

Link to section in online textbook.

First, watch this video to learn about what is necessary to construct a linear function.

This objective will focus on constructing linear functions from a point and slope or from two points.

Find the equation of the line containing the two points below. Write the equation in slope-intercept form.
$(\sage {pointOne1[0]}, \sage {pointOne1[1]}) \text { and } (\sage {pointTwo1[0]}, \sage {pointTwo1[1]})$

$y = \answer [tolerance=0.05]{\sage {solution1[0]}}x$ $+ \answer [tolerance=0.05]{\sage {solution1[1]}}$

To construct a linear function, we need its slope and a single point on the line. Can we figure out the slope from two points?

Find the equation of the line containing the two points below. Write the equation in slope-intercept form.
$(\sage {pointOne2[0]}, \sage {pointOne2[1]}) \text { and } (\sage {pointTwo2[0]}, \sage {pointTwo2[1]})$

$y = \answer [tolerance=0.05]{\sage {solution2[0]}}x$ $+ \answer [tolerance=0.05]{\sage {solution2[1]}}$

Find the equation of the line containing the two points below. Write the equation in slope-intercept form.
$(\sage {pointOne3[0]}, \sage {pointOne3[1]}) \text { and } (\sage {pointTwo3[0]}, \sage {pointTwo3[1]})$

$y = \answer [tolerance=0.05]{\sage {solution3[0]}}x$ $+ \answer [tolerance=0.05]{\sage {solution3[1]}}$

For these problems, you’ll be given a description of the line and a point. Think about what information you should get from the line, then use the point to construct a new linear function.

Find the equation of the line described below. Write the equation of the line in slope-intercept form.

Parallel to $\sage {standardForm4}=\sage {cCoeff4}$ and passing through the point $(\sage {point4[0]}, \sage {point4[1]})$ .

$y = \answer [tolerance=0.05]{\sage {solution4[0]}}x$ $+ \answer [tolerance=0.05]{\sage {solution4[1]}}$

If a line is parallel to another, what does that mean about its slope?

Find the equation of the line described below. Write the equation of the line in slope-intercept form.

Parallel to $\sage {standardForm5}=\sage {cCoeff5}$ and passing through the point $(\sage {point5[0]}, \sage {point5[1]})$ .

$y = \answer [tolerance=0.05]{\sage {solution5[0]}}x$ $+ \answer [tolerance=0.05]{\sage {solution5[1]}}$

Find the equation of the line described below. Write the equation of the line in slope-intercept form.

Perpendicular to $\sage {standardForm6}=\sage {cCoeff6}$ and passing through the point $(\sage {point6[0]}, \sage {point6[1]})$ .

$y = \answer [tolerance=0.05]{\sage {solution6[0]}}x$ $+ \answer [tolerance=0.05]{\sage {solution6[1]}}$

If a line is perpendicular to another, what does that mean about its slope?

Find the equation of the line described below. Write the equation of the line in slope-intercept form.

Perpendicular to $\sage {standardForm7}=\sage {cCoeff7}$ and passing through the point $(\sage {point7[0]}, \sage {point7[1]})$ .

$y = \answer [tolerance=0.05]{\sage {solution7[0]}}x$ $+ \answer [tolerance=0.05]{\sage {solution7[1]}}$