Question

1. Which of the following inequalities matches the graph?

graph of an inequality with a solid line through the points (-2, 0) and (0, 3) with shading below the line

y < 1 over 3 x + 3
y less than or greater to 3 over 2 x + 3
y greater than or equal to 3 over 2 x + 3
The correct inequality is not listed.

Answer 1

a solid line indicates that there is an equal sign in the problem
shading below the line indicates a less then sign is used.

Now let us find the slope by using the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
(-2,0)...x1 = -2 and y1 = 0
(0,3)...x2 = 0 and y2 = 3
now we sub
slope(m) = (3 - 0) / (0 - (-2)
slope(m) = 3/(0 + 2)
slope(m) = 3/2

Now use y = mx + b form...and since we already found the slope(m), we need to find the y intercept(b).
y = mx + b
slope(m) = 3/2
use either of your points (0,3)...x = 0 and y = 3
now sub and find b
3 = 3/2(0) + b
3 = b

so your equation is : y = 3/2x + 3....but remember what I said before, a solid line indicates an equal sign and shading below the line indicates less then.
Therefore, your inequality is : y <= 3/2x + 3

Answer 2

Its choice B?

Answer 3

@texaschic101