ImurGirlfriend53
contestada

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.

Respuesta :

calculista

we have

[tex]y=\frac{1}{3}x-2[/tex]

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 [tex](0,0)[/tex] is not a solution of the equation

Verify

Substitute the value of x and y in the equation

[tex]0=\frac{1}{3}*0-2[/tex]

[tex]0=-2[/tex] ------> is not true

the point [tex](0,0)[/tex] is not a solution

therefore

The line does not pass through the origin

case C) The line passes through the point  [tex](0,-2)[/tex]

The statement is True

Because the point [tex](0,-2)[/tex] is a solution of the equation

Verify

Substitute the value of x and y in the equation

[tex]-2=\frac{1}{3}*0-2[/tex]

[tex]-2=-2[/tex] ------> is true

the point [tex](0,-2)[/tex] is a solution

therefore

The line passes through the point [tex](0,-2)[/tex]

case D) The slope of the line is [tex]3[/tex]

The statement is False

Because, the slope of the line is [tex]m=\frac{1}{3}[/tex]

case E) The y-intercept of the line is [tex]2[/tex]

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 [tex]x=0[/tex]

find the value of y

[tex]y=\frac{1}{3}*0-2=-2[/tex]

the y-intercept is equal to [tex]-2[/tex]


Ver imagen calculista

Answer:

Option A and Option C are true.

Step-by-step explanation:

Equation : [tex]y = \frac{1}{3}x-2[/tex]

General form of equation of straight line : [tex]y =mx+c[/tex] --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,[tex]y = \frac{1}{3}(0)-2[/tex]

[tex]y = -2[/tex]

So, False

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

Plug x = 0 in equation

So,[tex]y = \frac{1}{3}(0)-2[/tex]

[tex]y = -2[/tex]

So, True

D)The slope of the line is 3.

On comparing with 1

Slope = [tex]\frac{1}{3}[/tex]

So, False.

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

To calculate the y intercept  

Plug x = 0 in equation

So,[tex]y = \frac{1}{3}(0)-2[/tex]

[tex]y = -2[/tex]

So, False

Hence Option A and Option C are true.

Otras preguntas