Question

Stella graphs the equation y=1/3x – 2

Select ALL statements about Stella's graph that are true.

A The graph is a straight line.

B The line passes through the origin.

C The line passes through the point (0, –2)

D The slope of the line is 3.

E The y-intercept of the line is 2.

Answer 1

we have

`y=(1)/(3)x-2`

Statements

case A) The graph is a straight line.

The statement is True

Because, this is a linear equation (see the attached figure)

case B) The line passes through the origin.

The statement is False

Because the point
`(0,0)` is not a solution of the equation

Verify

Substitute the value of x and y in the equation

`0=(1)/(3)*0-2`

`0=-2` ------> is not true

the point
`(0,0)` is not a solution

therefore

The line does not pass through the origin

case C) The line passes through the point
`(0,-2)`

The statement is True

Because the point
`(0,-2)` is a solution of the equation

Verify

Substitute the value of x and y in the equation

`-2=(1)/(3)*0-2`

`-2=-2` ------> is true

the point
`(0,-2)` is a solution

therefore

The line passes through the point
`(0,-2)`

case D) The slope of the line is
`3`

The statement is False

Because, the slope of the line is
`m=(1)/(3)`

case E) The y-intercept of the line is
`2`

The statement is False

we know that

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

so

For
`x=0`

find the value of y

`y=(1)/(3)*0-2=-2`

the y-intercept is equal to
`-2`

Answer 2

Option A and Option C are true.

Explanation:

Equation :
`y = (1)/(3)x-2`

General form of equation of straight line :
`y =mx+c` --1

where m is the slope of line

A)The graph is a straight line.

True . It is in the form of equation of straight line.

B)The line passes through the origin.

Origin = (0,0)

Plug x = 0 in equation

So,
`y = (1)/(3)(0)-2`

`y = -2`

So, False

C)The line passes through the point (0, –2)

Plug x = 0 in equation

So,
`y = (1)/(3)(0)-2`

`y = -2`

So, True

D)The slope of the line is 3.

On comparing with 1

Slope =
`(1)/(3)`

So, False.

E)The y-intercept of the line is 2.

To calculate the y intercept

Plug x = 0 in equation

So,
`y = (1)/(3)(0)-2`

`y = -2`

So, False

Hence Option A and Option C are true.