The graph below shows the solution to a system of inequalities: Solid line joining ordered pairs 0, 3.75 and 15, 0. Shade the portion of the graph above the line in the first and second quadrant Which of the following inequalities is modeled by the graph? x + 4y ≥ 15; y ≥ 0 x − 4y ≥ 15; y ≥ 0 x + 4y ≤ 15; y ≥ 0 −x − 4y ≥ 15; y ≥ 0

(0,3.75)(15,0)
slope(m) = (0 - 3.75) / (15 - 0) = -3.75/15 = - 0.25 or -1/4

y = mx + b
slope(m) = -1/4
(15,0)...x = 15 and y = 0
now we sub
0 = -1/4(15) + b
0 = -15/4 + b
15/4 = b

y = -1/4x + 15/4
1/4x + y = 15/4....multiply by 4
x + 4y = 15.....and since it is a solid line, it contains an equal sign...and since it is shaded above the line, it is greater.
so ur inequality is : x + 4y > = 15 (thats greater then or equal)

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MrRoyal MrRoyal · Answer 2 · 2021-12-23T23:02:02-05:00

The inequalities that are modeled by the graph are \(x + 4y \ge 15\) and \(y \ge 0\)

The points on the solid line are given as: (0,3.75) and (15,0)

Start by calculating the slope (m)

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m = \frac{0 -3.75}{15 -0}\)

Simplify

\(m = -\frac{3.75}{15}\)

Divide

\(m = -0.25\)

Assume the linear inequality is a linear equation represented as:

\(y = m(x -x_1)+y_1\)

So, we have:

\(y = -0.25(x -0)+3.75\)

Open brackets

\(y = -0.25x+3.75\)

The shaded region is above the solid line; so, the linear equation becomes:

\(y \ge -0.25x+3.75\)

Multiply through by 4

\(4y \ge -x + 15\)

Add x to both sides

\(x + 4y \ge 15\)

Hence, the inequalities that are modeled by the graph are \(x + 4y \ge 15\) and \(y \ge 0\)