Question

Which graph represents a line with a slope of -2/3

and a y-intercept equal to that of the line y=2/3x-2 ?

Answer 1

`y=-(2)/(3) x-2`

Explanation:

the general equation for a line is:

`y=mx+b`

where
`m` is the slope of the line, and
`b` is the y-intercept.

Since we need a slope of -2/3:

`m=-(2)/(3)`,

So far we have that the line must have the equation:

`y=-(2)/(3) x+b`

the graph of a line with a negative slope is one that "falls" from left to right in the plane. And the number
`(2)/(3)` means that it falls at a ratio of 2 units in the y-axis for every 3 in the x-axis.

we are told that the y-intercept is that of the line:

`y=(2)/(3) x-2` --> here the y-intercept is -2.

Thus the equation of the line we are looking for is:

`y=-(2)/(3) x-2`

which means that this line crosses the y-axis at -2, and the graph is the one in the attached image.