standard_description: Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
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