Question

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded. Which system of linear inequalities is represented by the graph? y > x – 2 and x – 2y < 4 y > x + 2 and x + 2y < 4 y > x – 2 and x + 2y < 4 y > x – 2 and x + 2y < –4

Answer 1

17 1st option

35 2nd option

Explanation:

Answer 2

`y\geq x-2`

`x+2y<4`

Explanation:

step 1

Find the equation of the first inequality

Find the equation of the first solid line

we have the ordered pairs

(0,-2) and (2,0)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(0+2)/(2-0)`

`m=(2)/(2)`

`m=1`

The equation in slope intercept form is equal to

`y=mx+b`

we have

`m=1`

`b=-2` ---> the y-intercept is given

substitute

`y=x-2`

Remember that

Everything to the left of the solid line is shaded

so

The inequality is

`y\geq x-2`

step 2

Find the equation of the second inequality

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(0-2)/(4-0)`

`m=(-2)/(4)`

`m=-(1)/(2)`

The equation in slope intercept form is equal to

`y=mx+b`

we have

`m=-(1)/(2)`

`b=2` ---> the y-intercept is given

substitute

`y=-(1)/(2)x+2`

Remember that

Everything below and to the left of the line is shaded

so

The inequality is

`y<-(1)/(2)x+2`

Rewrite

Multiply by 2 both sides

`2y<-x+4`

`x+2y<4`

therefore

The system of inequalities is

`y\geq x-2`

`x+2y<4`

see the attached figure to better understand the problem