standard_description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
problem_activity: Warm-up
The purpose of this warm-up is for students to practice solving an equation for an unknown value while thinking about a coordinate pair,
\((x,y)\)
, that makes the equation true. While the steps to solve the equation are the same regardless of which value of
\(x\)
students choose, there are strategic choices that make solving the resulting equation simpler. This should be highlighted in the discussion.
Launch
Encourage students to not pick 0 for
\(x\)
each time.
Student Facing
For each equation choose a value for
\(x\)
and then solve to find the corresponding
\(y\)
value that makes that equation true.
\(6x=7y\)
\(5x+3y=9\)
\(y+5-\frac13 x=7\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Collect the pairs of
\(x\)
’s and
\(y\)
’s students calculated and graph them on a set of axes. For each equation, they form a different line. Have students share how they picked their
\(x\)
values. For example:
For the first problem, choosing
\(x\)
to be a multiple of 7 makes
\(y\)
an integer.
For the last problem, picking
\(x\)
to be a multiple of 3 makes
\(y\)
an integer.


aligns: no