Question

Find the inequality represented by the graph.

Answer 1

`y\le -(1)/(3)x + 1`

Explanation:

The equation of the line is y = mx + b

where

m is the slope = rise/run

b = y-intercept ie where the line crosses the y-axis at x = 0

The line crosses the y axis at y = 1 so the y-intercept is 1 and the point at which the line crosses is (0, 1)

We have the equation as

y = mx + 1

To find the slope, take any two points on the line. Find the corresponding difference in the y values and divide this difference by the corresponding difference in the x values

Two convenient points are (0, 1) and (3, 0)

Slope =
`(0-1)/(3-0) = -(1)/(3)`

Equation of the line :

`y = -(1)/(3)x + 1`

To find out if the inequality in the shaded region is a ≥ or a ≤ inequality, take a point in the shaded region. Determine whether the chosen point x, y values satisfy which of the following equations

`y\le -(1)/(3)x + 1` (1)

or

`y\ge -(1)/(3)x + 1` (2)

The point (0,0) is inside the shaded region

Plug in these values into inequality (1)

`0 = -(1)/(3)\cdot0 + 1` = 1

Is 0 ≤ 1 ?

Indeed it is so the inequality is

`y\le -(1)/(3)x + 1` (Answer)

The region on the opposite side of the line must be a ≥ inqeuality

The attached graph makes it clearer