standard_description: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Activity
The purpose of this activity is for students to practice identifying the parts of a linear equation that affect specific features of its graph, specifically the slope and
\(y\)
-intercept. This will be useful when students make connections between two-variable linear equations and their graphs and situations that they represent in an associated Algebra 1 lesson.
Student Facing
For each equation, identify the slope and
\(y\)
-intercept of its graph.
\(y = 3x-8\)
\(y = 10-2x\)
\(y = \frac{x}{2} + 1\)
\(y + 1 = 9x\)
\(y = \frac{1}{3}(9x + 12)\)
Student Response
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Activity Synthesis
Discuss the slopes and
\(y\)
-intercepts and how they can be used. Here are discussion questions:
"How do you find the slope and
\(y\)
-intercept for the graph of a linear equation written in standard form like
\(\text-3x+y=\text-8\)
?" (Substitute 0 for
\(x\)
and solve for
\(y\)
.)
"The rate of change in a situation corresponds to what part of the graph?" (The rate of change corresponds to the slope of a graph.)
"Why is it useful to know the
\(y\)
-intercept and slope?" (The
\(y\)
-intercept and slope can make it very easy to create a graph from an equation because we know the key features. Also, they are useful to know in understanding a situation and the relationships between each quantity involved.)


aligns: no