Question

The table shows some of the solutions for an inequality related to the line shown in the graph. Which inequality describes the solution set?

Answer 1

The answer is y ≥ x - 3 ⇒ answer (A)

Explanation:

* A first we must find the equation of the line

- Lets calculate the slope of the line using any two

points from the graph

∵ (0 , -3) and (3 , 0) o the line

∵ The rule of the slope is (y2 - y1)/(x2 - x1)

∴ m = (0 - -3)/(3 - 0) = 3/3 = 1

∵ The form of the equation is y = mx + c, where m is the slope

and c is the y-intercept

∵ The line cut the y-axis at point (0 , -3)

∴ c = -3

∴ The equation of the line is y = x - 3

* To change to inequality you must to know y ≥ or ≤

- Note: we used ≤ or ≥ because the line is solid (not doted)

- From the table

# The solution (-1 , -3) is over the line

# The solution (0 , -1) is on the line

# The solution (2 , -1) is on the line

# The solution (3 , 1) is over the line

∴ The inequality is y ≥ x - 3

* The answer is (A)