Question

PLEASE HELP! 90 POINTS!!!

4.) Select all statements that are true about the linear equation.

y=1/2x−4

A.)The point (−6,7) is on the graph of the equation.

B.)The point (−4,−6) is on the graph of the equation.

C.)The graph of the equation is a single point representing one solution to the equation.

D.)The graph of the equation is the set of all points that are solutions to the equation.


7.) Use the Line Tool to graph the equation.

4x−6y=48

(see graph below)


9.) Use the Line Tool to graph the function.

f(x)=2/3x+1

(see graph below)

15.) Which answer is an equation in point-slope form for the given point and slope?

point: (−3,5) ; slope: 4


a.)y+5=4(x−3)

b.)y−5=4(x−3)

c.)y−5=4(x+3)

d.)y+5=4(x+3)


16.)Which ordered pairs are on the line ​ 4x−3y=8 ​?

Select each correct answer.


a. ​ (3/2,−2/3) ​

​b. (−1,4) ​

​c. (−4,−8) ​

​d. (1,−4/3) ​

Answer 1

Part 1) we have

`y=(1)/(2)x-4`

Statements

case A) The point
`(-6,7)` is on the graph of the equation

The statement is false

we know that

If the point is on the graph of the equation

then

the point must be satisfy the equation

Verify

Substitute the value of x and y in the equation

`7=(1)/(2)(-6)-4`

`7=-7` ------> is not true

therefore

the point is not on the graph

case B) The point
`(-4,-6)` is on the graph of the equation

The statement is true

we know that

If the point is on the graph of the equation

then

the point must be satisfy the equation

Verify

Substitute the value of x and y in the equation

`-6=(1)/(2)(-4)-4`

`-6=-6` ------> is true

therefore

the point is on the graph

case C) The graph of the equation is a single point representing one solution to the equation

The statement is false

Because, the graph of the equation is the set of all points that are solutions to the equation

case D) The graph of the equation is the set of all points that are solutions to the equation

The statement is true

The graph of the equation is the set of all points that satisfy the equation

Part 2) Graph the equation

`4x-6y=48`

Find the intercepts of the equation

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

For
`x=0`

`4*0-6y=48`

`y=-8` -------> y-intercept
`(0,-8)`

For
`y=0`

`4x-6*0=48`

`x=12` -------> x-intercept
`(12,0)`

Plot the x-intercept and the y-intercept to graph the line

see the attached figure N
`1`

The answer Part 2) in the attached figure N
`1`

Part 3) Graph the function

`f(x)=(2/3)x+1`

Find the intercepts of the equation

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

For
`x=0`

`f(0)=(2/3)*0+1`

`f(0)=1` -------> y-intercept
`(0,1)`

For
`f(x)=0`

`0=(2/3)x+1`

`x=-1.5` -------> x-intercept
`(-1.5,0)`

Plot the x-intercept and the y-intercept to graph the line

see the attached figure N
`2`

The answer Part 3) in the attached figure N
`2`

Part 4) Which answer is an equation in point-slope form for the given point and slope?

point:
`(-3,5)` ; slope:
`4`

we know that

the equation of the line in point-slope form is equal to

`y-y1=m(x-x1)`

Substitute the values

`y-5=4(x+3)`

therefore

The answer part 4) is the option C

`y-5=4(x+3)`

Part 5) Which ordered pairs are on the line ​
`4x-3y=8` ​?

we know that

If a point is on the line

then

the point must be satisfy the equation of the line

we're going to verify every case

case A)
`(3/2,-2/3)`

Substitute the value of x and y in the equation of the line

`4*(3/2)-3*(-2/3)=8`

`6+2=8`

`8=8` -------> is true

therefore

the point
`(3/2,-2/3)` is on the line

case B)
`(-1,4)`

Substitute the value of x and y in the equation of the line

`4*(-1)-3*(4)=8`

`-4-12=8`

`-16=8` -------> is not true

therefore

the point
`(-1,4)` is not on the line

case C)
`(-4,-8)`

Substitute the value of x and y in the equation of the line

`4*(-4)-3*(-8)=8`

`-16+24=8`

`8=8` -------> is true

therefore

the point
`(-4,-8)` is on the line

case D)
`(1,-4/3)`

Substitute the value of x and y in the equation of the line

`4*(1)-3*(-4/3)=8`

`4+4=8`

`8=8` -------> is true

therefore

the point
`(1,-4/3)` is on the line

therefore

the answer Part 5) is

`(3/2,-2/3)`

`(-4,-8)`

`(1,-4/3)`