Question

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 1, negative 3) and (0, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 3) and (1, negative 3). Everything to the right of the line is shaded.

A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph?

y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1

Answer 1

y > 3x

y > -2x -1 if the line is a broken line and y
`\geq` -2x -1 if the line is a solid line

Explanation:

(-1,-3) (0,0) This line is proportional because it goes though the origin (0,0), so the slope is
`(-3)/(-1)` = 3. The y intercept is o

y > 3x

(-2,3) (1, -3)

The slope
`(-3- 3)/(1 -(-2))` =
`(-6)/(3)` = -2

-3 = (-2)(1) + b

-3 = -2 + b Add 2 to both sides

-1 = b

y = -2x - 1

I am assuming that there is a lot you know. If this does not make sense, it is me and not you. I just did not go deep enough in my explanation.

Helping in the name of Jesus.