Line segments sp has an equation of y=2x+3

what are the other equations of the line segments forming the 3 other sides of the rectangle?

show work

Answer with Step-by-step explanation:

We are given that

Equation of line segment SP =

We have to find the equations of the line segments forming the 3 other sides of a rectangle.

Substitute the x=0 in given equation

Then, we get

Substitute y=0 then, we get

Hence, the equation of line segment SP passing from the point (0,3) and (-1.5,0).

By comparing withe y=mx+c

We get m=2=Slope of line segment SP

The line segment SR is perpendicular to the line segment SP and passing form the point (-1.5,0).

Slope of line segment SR=

Because when two lines are perpendicular then the relation between the slopes of two lines is given by

The equation of line segment of SR is given by

The equation of line segment SR with slope -1/2 and passing from the point (-1.5,0) is given by

Line segment RQ is parallel to SP

So,Slope of line RQ=2

Because when two lines are parallel then their slope are equal.

Line segment PQ is perpendicular to SP

Therefore, slope of PQ=

The equation of line segment PQ with slope -1/2 and passing through the point (0,3) is given  by

Substitute x=0 in

Then, we get y=-0.75

The equation of line segment RQ with slope 2 parallel to SP and passing through the point (0,-0.75)is given by

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.