Question 1 (multiple choice worth 1 points)

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.

question 2 (multiple choice worth 1 points)

which of the following inequalities matches the graph?

graph of an inequality with a dashed line through the points (0, -5) and (5, 10) with shading above the line

y greater than or equal to 3x - 5

y < 3x - 5

y < 1 over 3x - 5

the correct inequality is not listed.

1) First, find the equation of the line

y = mx + b

m = slope = rise / run = [3-0] / [0 - (-2)] = 3/2
b = y-intercept = 3

Then, y = [3/2]x + 3

Now, given that the solution is the set of points in the line and below the line, y hast to be less or equal than the function: y ≤ [3/2]x + 3

That is the third option.

2) First find the equation of the line

y = mx + b

m = [10 - (-5)] / [5 - 0] = 15 / 5 = 3
b = - 5
y = 3x - 5

Now, given that the solution is the set of points above the line, the solution are the y greater than the function: y > 3x - 5.

I do not see that inequality in the list. (Notice that I interpret that the dash line means that the points in the line are not part of the solution, that is why I use > instead of greater than or equal to)