Question

50 POINTS FOR CORRECT AWNSER!

Answer 1

`\mathsf{y < \frac47x-4}`

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=(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=(0-(-4))/(7-0)=\frac47}`

Therefore, the equation of the line is:

`\mathsf{y=\frac47x-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 < \frac47x-4}`