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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.

Verified Answer :

calculista

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 \(-2\)


View image calculista

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.

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