Compare linear functions represented in different ways.
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In Lessons 9 and 10 of Unit 4, students compared functions by looking at the rates of change and initial values of those functions. This lesson revisits some of those concepts, but looks specifically at linear functions and describes the graphs of these functions by the slope and $$y$$-intercept of the line.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.
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Three linear functions are represented below.
Three friends participate in the loyalty program at a local coffee shop. A participant in the program earns points for each visit that can be used to get drinks and food for free. The graph below shows the point balances of the three friends over several weeks.
Line L goes through the points (4, 9) and (-4, -7). Line M has a $$y-$$intercept that is greater than line L.
What could be the equation for line M?
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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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Linear function $$K$$ is represented by the equation $${y={1\over2}x-2}$$.
Draw the graph of a line that has a greater slope than function $$K$$ and the same $$y$$-intercept as function $$K$$.