Question

Stella graphs the equation y=1/3x – 2

Answer 1

we have

$y=\frac{1}{3}x-2$

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

$0=\frac{1}{3}*0-2$

$0=-2$ ------> 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

$-2=\frac{1}{3}*0-2$

$-2=-2$ ------> 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 $m=\frac{1}{3}$

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

$y=\frac{1}{3}*0-2=-2$

the y-intercept is equal to $-2$

Answer 2

Answer:

Option A and Option C are true.

Step-by-step explanation:

Equation : $y = \frac{1}{3}x-2$

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,$y = \frac{1}{3}(0)-2$

$y = -2$

So, False

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

Plug x = 0 in equation

So,$y = \frac{1}{3}(0)-2$

$y = -2$

So, True

D)The slope of the line is 3.

On comparing with 1

Slope = $\frac{1}{3}$

So, False.

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

To calculate the y intercept  

Plug x = 0 in equation

So,$y = \frac{1}{3}(0)-2$

$y = -2$

So, False

Hence Option A and Option C are true.