Question

Use the drawing tools to form the correct answer on the graph. Draw a point that belongs to the solution region of this system of inequalities.

Answer 1

#1

• y>1.5^x+4

Find y intercept

• y>1+4
• y>5

#2

• y<2/3x+6

Y intercept

• y<6

Both graphs attached

An point should be (1,6)

Answer 2

Answer:

< or > = dashed line

≤ or ≥ = solid line

< or ≤ = shade below the line

> or ≥ = shade above the line

To draw:

$y < \dfrac{2}{3}x+6$

Treat as a linear equation.

Find 2 points:

$x=0 \implies y=\dfrac{2}{3}(0)+6=6 \implies (0,6)$

$x=3 \implies y=\dfrac{2}{3}(3)+6=8 \implies (3,8)$

Plot the 2 points and draw a dashed straight line through them.

To draw:

$y > 1.5^x+4$

Treat as an exponential equation.

Find y-intercept:

$x=0\implies y=1.5^0+4=5\implies (0,5)$

End behaviors:

$\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty$

$\textsf{As } x \rightarrow - \infty, f(x) \rightarrow 4$

Draw the curve as a dashed line.

Once both lines are drawn, shade the overlapping region below the linear inequality and above the exponential inequality.  

A point that belongs to the solution is any point in the shaded area,
e.g. (1, 6)