8) give the equation of the blue line, the red line, a line that is parallel to the red line and a line that is perpendicular to the red line. (4 points)

Blue - y=-2

Red-

Parallel to Red-

Perpendicular to Red-

Step-by-step explanation:

The slope intercept of a line is y=mx +b where

The Blue line intercepts the y-axis at -2 so b=-2. It has no vertical change since it is a horizontal line. This means the slope, m, is 0. m=0. It's equation is y=0x-2

y=0-2 since anything times 0 is 0.

y=-2.

The red line intercepts the y-axis at 2 so b=2. It intercepts the x-axis at (-3,0). Between these two intercepts we can find the slope:

Slope:

We substitute and

The red line has equation .

Parallel lines have the same slope with a different y-intercept. So we write a line where m=2/3 and b is something else.

Perpendicular lines have a negative reciprocal slope to the original. So we write the line where m/-3/2.

answer: 12

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is