Question

Use the graph to answer the Exercises 36 and 37​

Answer 1

Answer 36:

y>(-1)x+2

$y\geq 4x$

Answer 37:

The point of intersection is ($\frac{2}{5}$,$\frac{8}{5}$)

Step-by-step 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=$\frac{Y2-Y1}{X2-X1}$

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=$\frac{Y2-Y1}{X2-X1}$

m=$\frac{2-0}{0-2}$

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=$\frac{Y2-Y1}{X2-X1}$

m=$\frac{4-0}{1-0}$

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=$\frac{2}{5}$

y=4x=4$\frac{2}{5}$

y=$\frac{8}{5}$

Thus, The point of intersection is ($\frac{2}{5}$,$\frac{8}{5}$)

Answer 37:

The point of intersection is ($\frac{2}{5}$,$\frac{8}{5}$)