Question

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

Answer 1

Answer:

$y=-\frac{2}{3} x-2$

Step-by-step 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:

$m=-\frac{2}{3}$,

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

$y=-\frac{2}{3} x+b$

the graph of a line with a negative slope is one that "falls" from left to right in the plane. And the number $\frac{2}{3}$ 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:

$y=\frac{2}{3} x-2$ --> here the y-intercept is -2.

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

$y=-\frac{2}{3} x-2$

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