Question

Stella graphs the equation y=13x – 2y=13x – 2 .

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



The graph is a straight line.

The line passes through the origin.

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

The slope of the line is 3.

The y-intercept of the line is 2.

Answer 1

we have

`y=13x-2`

Statements

case A) The graph is a straight line.

The statement is True

Because, this is a linear equation of the form
`y=mx+b`

where

m is the slope

b is the y-intercept

In this problem

`m=13\ b=-2`

case B) The line passes through the origin

The statement is False

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

Verify

Substitute the values of
`x=0` and
`y=0` in the equation

`0=13*0-2`

`0=-2` -------> is not true (the point not lie on the line)

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

The statement is True

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

Verify

Substitute the values of
`x=0` and
`y=-2` in the equation

`-2=13*0-2`

`-2=-2` -------> is true (the point lie on the line)

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

The statement is False

Because the slope of the line is
`m=13`

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

The statement is False

Because

we know that

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

Substitute the value of
`x=0` in the equation and find the value of y

`y=13*0-2`

`y=-2`

therefore

the y-intercept of the line is
`-2`

the answer is

The graph is a straight line.

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

see the attached figure to better understand the problem

Answer 2

y = 13x - 2

the graph is a straight line...TRUE
the line passes thru the origin (0,0)....FALSE
the line passes thru the points (0,-2)...TRUE
the slope of the line is 3...FALSE...the slope is 13
the y int of the line is 2....FALSE...the y int is -2