Question

50 POINTS FOR CORRECT AWNSER!

Answer 1

Answer:

$\mathsf{y < \dfrac47x-4}$

Step-by-step explanation:

First, find the equation of the line.

Slope-intercept form of a linear equation:  $\mathsf{y=mx+b}$

(where m is the slope and b is the y-intercept)

From inspection of the graph, the y-intercept is at (0, -4)

Therefore, b = -4

Choose another point on the line, e.g. (7, 0)

Now use the slope formula to find the slope:

$\mathsf{slope=\dfrac{y_2-y_1}{x_2-x_1}}$

where:

• $\mathsf{(x_1,y_1)=(0,-4)}$
• $\mathsf{(x_2,y_2)=(7,0)}$

$\implies \mathsf{slope=\dfrac{0-(-4)}{7-0}=\dfrac47}$

Therefore, the equation of the line is:

$\mathsf{y=\dfrac47x-4}$

For an inequality, the dashed line means < or >  (whereas a solid line means ≤ or ≥)

As the shading is below the line, we need to use <

Therefore, the final inequality is:

$\mathsf{y < \dfrac47x-4}$