Answer 36:
y>(-1)x+2
[tex]y\geq 4x[/tex]
Answer 37:
The point of intersection is ([tex]\frac{2}{5}[/tex],[tex]\frac{8}{5}[/tex])
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=[tex]\frac{Y2-Y1}{X2-X1}[/tex]
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=[tex]\frac{Y2-Y1}{X2-X1}[/tex]
m=[tex]\frac{2-0}{0-2}[/tex]
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=[tex]\frac{Y2-Y1}{X2-X1}[/tex]
m=[tex]\frac{4-0}{1-0}[/tex]
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 [tex]y\geq 4x[/tex]
Now,
Take a random point from the shaded section of the graph
Let that point be (0,1)
Test that point,
[tex]y\geq 4x[/tex]
[tex]1\geq 4(0)[/tex]
[tex]1\geq 0[/tex]
True, The required inequality for a blue line is [tex]y\geq 4x[/tex]
Answer 36:
y>(-1)x+2
[tex]y\geq 4x[/tex]
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=[tex]\frac{2}{5}[/tex]
y=4x=4[tex]\frac{2}{5}[/tex]
y=[tex]\frac{8}{5}[/tex]
Thus, The point of intersection is ([tex]\frac{2}{5}[/tex],[tex]\frac{8}{5}[/tex])
Answer 37:
The point of intersection is ([tex]\frac{2}{5}[/tex],[tex]\frac{8}{5}[/tex])
