Question

graph the inequality.
$y > -4x - 3$

Explanation:

Step1: Identify boundary line

The inequality $y > -4x - 3$ has a boundary line $y = -4x - 3$. Since the inequality is $>$ (not $\geq$), the line will be dashed.

Step2: Find intercepts for plotting

• y-intercept: Set $x=0$, solve for $y$:

$y = -4(0) - 3 = -3$. So the point is $(0, -3)$.

• x-intercept: Set $y=0$, solve for $x$:

$0 = -4x - 3 \implies 4x = -3 \implies x = -\frac{3}{4} = -0.75$. So the point is $(-0.75, 0)$.

Step3: Test a point for shading

Choose the origin $(0,0)$ (not on the line):
Substitute into $y > -4x - 3$:
$0 > -4(0) - 3 \implies 0 > -3$, which is true. Shade the region containing $(0,0)$.

Answer:

1. Draw a dashed line through the points $(0, -3)$ and $(-0.75, 0)$ (representing $y=-4x-3$).
2. Shade the region of the coordinate plane that lies above this dashed line.