Question

Find the inequality represented by the graph.

Answer 1

`\displaystyle 3x - y > 4\:or\:y < 3x - 4`

Step-by-step Step-by-step explanation:

First, find the rate of change [slope]. From
`\displaystyle [1, -1],`travel three units south over one unit west, where you will arrive at the y-intercept of
`\displaystyle [0, -4].`Doing this will lead you to knowing that the rate of change is
`\displaystyle 3.` Moreover, you could have also done this with the rate of change formula:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ \\ (1 - 4)/(-1 \pm 0) \hookrightarrow (-3)/(-1) \\ \\ \boxed{3 = m}`

Here you are!

Now we insert this information into the Slope-Intercept formula, but BEFORE doing this, sinse we are dealing with the inequality version of the Slope-Intercept formula, we need to initiate the zero-interval test to determine the inequality symbol of the function. Here is how it is done:

`\displaystyle 0 < 3[0] - 4; \boxed{0 \\less -4} \\ 0 > 3[0] - 4; \boxed{0 > -4}`

Therefore, sinse this graph has a dashed line AND is not shaded in the area that contains the origin, the less than symbol is suitable for this function, which means the slope-intercept inequality is
`\displaystyle y < 3x - 4.`

I am joyous to assist you at any time.