Question

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph? y ≤ One-halfx + 2 y ≥ One-halfx + 2 y ≤ One-thirdx + 2 y ≥ One-thirdx + 2

Answer 1

Answer:

$y\le\dfrac{1}{2}x+2$

Step-by-step explanation:

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). This line has the equation

$y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\ \\y=\dfrac{1}{2}(x+4)\\ \\y=\dfrac{1}{2}x+2$

The origin belongs to the shaded region, so its coordinates must satisfy the inequality. Since

$\dfrac{1}{2}\cdot 0+2=2\ge 0,$

then the correct inequality is

$y\le\dfrac{1}{2}x+2$

Answer 2

Answer:

A

y ≤ $\frac{1}{2}$x + 2

Step-by-step explanation: