Answer:
[tex]\mathsf{y < \dfrac47x-4}[/tex]
Step-by-step explanation:
First, find the equation of the line.
Slope-intercept form of a linear equation: [tex]\mathsf{y=mx+b}[/tex]
(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:
[tex]\mathsf{slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where:
- [tex]\mathsf{(x_1,y_1)=(0,-4)}[/tex]
- [tex]\mathsf{(x_2,y_2)=(7,0)}[/tex]
[tex]\implies \mathsf{slope=\dfrac{0-(-4)}{7-0}=\dfrac47}[/tex]
Therefore, the equation of the line is:
[tex]\mathsf{y=\dfrac47x-4}[/tex]
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:
[tex]\mathsf{y < \dfrac47x-4}[/tex]
