Functions: Graphing Functions Practice MCQ

First, we determine the equation of the boundary line. This line includes points (0,3) and (8.0) , so the slope can be calculated as follows:

Since we also know the y-intercept is (0,3), we can substitute ${\displaystyle m=-<!--\; -\; -->\frac{3}{8},b=3}$ in the slope-intercept form to obtain the equation of the boundary line:

${\displaystyle y=mx+b}$

${\displaystyle y=-<!--\; -\; -->\frac{3}{8}x+3}$

The boundary is included, as is indicated by the line being solid, so the equality symbol is replaced by either ≤ or ≥. To find out which one, we can test a point in the solution set - for ease, we will choose (0,0):

y ____ ${\displaystyle -<!--\; -\; -->\frac{3}{8}x+3}$

0 ____ ${\displaystyle -<!--\; -\; -->\frac{3}{8}\cdot <!--\; \cdot \; -->0+3}$

0 ____ 3

0 is less than 3 so the correct symbol is ${\displaystyle \le <!--\; \le \; -->}$

The inequality is ${\displaystyle y\le <!--\; \le \; -->-<!--\; -\; -->\frac{3}{8}x+3}$