Write linear equations using two given points on the line.
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Lessons 11 and 12 address writing linear equations using information about the line or situation. In Lesson 12, students are given two points on the line or two solutions to a situation in order to determine the slope or rate of change and the $$y$$-intercept or initial value.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from discussion) and Anchor Problem 3 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.
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A line is shown in the coordinate plane below.
What is the equation for the line shown?
A line passes through the points (4, 3) and (9, -7).
What is the equation for this line in slope-intercept form?
A model airplane reaches a maximum altitude and then begins to descend at a constant rate in feet per second. After falling for 12 seconds, the model airplane has an altitude of 212 feet. After falling for 25 seconds, the model airplane’s altitude is 95 feet.
What function represents the altitude of the model airplane, $$y$$, after $$x$$ seconds of falling?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Tickets to a concert are available for early access on a special website. The website charges a fixed fee for early access to the tickets, and the tickets to the concert all cost the same amount with no additional tax. A friend of yours purchases 4 tickets on the website for a total of $162. Another friend purchases 7 tickets on the website for $270.
What function represents the total cost, $$y$$, for the purchase of $$x$$ tickets on the website?
Write an equation in slope-intercept form for the line that passes through the points $${(-2, -3)}$$ and $${(1, 12)}$$.