Question

Which of the following shows the graph of a line with a slope of 6/5 and a y intercept of -3?

Answer 1

The correct option is 1.

Explanation:

It is given that the slope of the line is 6/5 and y intercept is -3. It means the line must be passes through the point (0,-3).

The slope intercept form of a line is

`y=mx+b`

where, m is slope and b is y-intercept.

Substitute m=6/5 and b=-3 in the above equation to find the equation of line.

`y=(6)/(5)x+(-3)`

So, the equation of line is
`y=(6)/(5)x+(-3)`.

Substitute y=0 in the above equation to find the x-intercept of the line.

`0=(6)/(5)x-3`

Add 3 on both the sides.

`0+3=(6)/(5)x-3+3`

`3=(6)/(5)x`

Multiply both sides by 5.

`15=6x`

Divide both sides by 6.

`(15)/(6)=x`

`2.5=x`

The x-intercept of the line is 2.5. It means the line must be passes through the point (2.5,0).

Since only in graph 1, the line passes through the points (0,-3) and (2.5,0), therefore the graph 1 represents the required line and option 1 is correct.