graph the inequality on the axes below.\n5x + 4y < -16

Explanation:

Step1: Rewrite in slope - intercept form

First, solve $5x + 4y < - 16$ for $y$. Subtract $5x$ from both sides: $4y<-5x - 16$. Then divide by 4: $y<-\frac{5}{4}x - 4$.

Step2: Find the boundary line

The boundary line of the inequality $y<-\frac{5}{4}x - 4$ is the equation $y =-\frac{5}{4}x - 4$. The y - intercept is $b=-4$ (the point $(0, - 4)$) and the slope $m =-\frac{5}{4}$.

Step3: Determine the type of line

Since the inequality is $y<-\frac{5}{4}x - 4$ (strict inequality), the boundary line is a dashed line.

Step4: Test a point

Choose a test - point not on the line, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the original inequality: $5(0)+4(0)<-16$, which is $0 < - 16$, a false statement. So, shade the region that does not contain the point $(0,0)$.

To graph:

1. Plot the y - intercept at the point $(0,-4)$.
2. Use the slope $-\frac{5}{4}$ to find another point. From $(0,-4)$, move 4 units to the right and 5 units down to get the point $(4,-9)$.
3. Draw a dashed line through the points $(0,-4)$ and $(4,-9)$.
4. Shade the region below the dashed line.

Answer:

Graph a dashed line $y =-\frac{5}{4}x - 4$ and shade the region below the line.