HSA.REI.D.12 Tutor Intake — Graphing Linear Inequalities

When graphing the inequality $y < 3x + 1$, what type of boundary line
should be drawn, and why?

After drawing the boundary line for $y \geq 2x - 3$, a student needs
to decide which side to shade.

They test the origin $(0, 0)$: $0 \geq 2(0) - 3 \Rightarrow 0 \geq -3$. True.

Which region should be shaded?

A system of two linear inequalities is graphed. The solution region for
the system is the set of all points that satisfy:

Which inequality has a solid boundary line and shading above the line?

Test whether the point $(-2, 0)$ satisfies the inequality $3x + y \leq 2$.

Substitute: $3(-2) + 0 = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

Does $(-2, 0)$ satisfy $3x + y \leq 2$? Enter yes or no:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

A shaded half-plane has a solid boundary line passing through $(0, 1)$
and $(2, 3)$, with shading below the line.

The boundary line has slope $m = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   and $y$-intercept $= $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
The inequality (using $\leq$) is: $y$   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲     ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   $x + $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲