Question

Use the graph to answer the Exercises 36 and 37
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Answer 1

Answer 36:

y>(-1)x+2

`y\geq 4x`

Answer 37:

The point of intersection is (
`(2)/(5)`,
`(8)/(5)`)

Explanation:

Given graph show shaded area of inequality

The equation of a line is given by y=mx+c

where m is the slope of line and c is y-intercept of a line

The slope is given by m=
`(Y2-Y1)/(X2-X1)`

For the red line:

Here, Redline is passing through the point (2,0) and (0,2)

The slope of the red line will be

m=
`(Y2-Y1)/(X2-X1)`

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

m=(-1)

and y-intercept of the line is c=2

The equation of the red line is given by

y=mx+c

y=(-1)x+2

To find which inequality holds true for the red line

Let inequality for red line be y>(-1)x+2

Now,

Take a random point from the shaded section of the graph

Let that point be (2,1)

Test that point,

y>(-1)x+2

1>(-1)2+2

1>0

True, The required inequality for a red line is y>(-1)x+2

For the blue line:

Here,blue line is passing through the point (0,0) and (1,4)

The slope of the red line will be

m=
`(Y2-Y1)/(X2-X1)`

m=
`(4-0)/(1-0)`

m=4

and y-intercept of the line is c=0

The equation of the blue line is given by

y=mx+c

y=4x

To find which inequality holds true for the blue line

Let inequality for blue line be
`y\geq 4x`

Now,

Take a random point from the shaded section of the graph

Let that point be (0,1)

Test that point,

`y\geq 4x`

`1\geq 4(0)`

`1\geq 0`

True, The required inequality for a blue line is
`y\geq 4x`

Answer 36:

y>(-1)x+2

`y\geq 4x`

To find a point of intersection of system of the equation:

Equation 1: y=(-1)x+2

Equation 2: y=4x

Replacing value of y in the equation 1

we get

y=(-1)x+2

4x=(-1)x+2

5x=2

x=
`(2)/(5)`

y=4x=4
`(2)/(5)`

y=
`(8)/(5)`

Thus, The point of intersection is (
`(2)/(5)`,
`(8)/(5)`)

Answer 37:

The point of intersection is (
`(2)/(5)`,
`(8)/(5)`)