Question

2. Which inequality is graphed below? A) - 4x + 3y:9 B) - 4x + 3y=9 C) 4x – 3y 12

Answer 1

To identify the inequality graphed you need to identify the equation of the line that limits the inequality:

To identify the equiation of the line you need to dinf the slope:

Use two points on the line: (0 , - 4) and (3,0)

Formula to find the slope:

`m=(y_2-y_1)/(x_2-x_1)`
`m=(0-(-4))/(3-0)=(4)/(3)`

The y - intercept (b) is the value of y when x=0 in this case the b is -4

You have the equation in slope-interpcept form:

`\begin{gathered} y=mx+b \\ \\ y=(4)/(3)x-4 \end{gathered}`

Substract -4/3 x in btoh sides of the equation:

`\begin{gathered} y-(4)/(3)x=(4)/(3)x-(4)/(3)x-4 \\ \\ y-(4)/(3)x=-4 \end{gathered}`

Multiply both sides of the equation by 3:

`3y-4x=-12`

Multiply for -1 both sides of the equation:

Equation of the line:

`4x-3y=12`As the shadow area is under the line the inequality is:
`4x-3y\leq12`