Question

This graph shows the solution to which inequality?

Answer 1

Answer:

$y > \frac{1}{3}x - 2$

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope, and b is the y-intercept(value of y when x = 0).

In this question:

We have that when $x = 0, y = -2$. So the line is given by:

$y = mx - 2$

Finding the slope:

We have two points in the line, which are (-3,-3) and (3,-1). The slope is given by the change in y divided by the change in x. So

Change in y: -1 - (-3) = -1 + 3 = 2

Change in x: 3 - (-3) = 3 + 3 = 6

Slope: $m = \frac{2}{6} = \frac{1}{3}$

Solution to the inequality:

The solution to this inequality is all the points above the dashed line, which means that the dashed line is not part of the solution. So

$y > \frac{1}{3}x - 2$