Question

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below and to the right of the line is shaded. Which linear inequality is represented by the graph? y ≤ 2x + 4 y ≤ one-halfx + 3 y ≥ One-halfx + 3 y ≥ 2x + 3

Answer 1

Answer: $y \leq \frac{1}{2} x+3$

Step-by-step explanation:

If a function has a positive slope, that means the y value is increasing with respect to x. As you go down the x-axis, the y value will continuously increase.

First you want to plot the two sets of coords that they gave you, or else you wont know what the line looks like. Or, you could visually do it in your head. We're going down -4 on the x-axis and down 1 on the y-axis. Then for our second coords, we are going to 0 on the x-axis, then up 3 on the y-axis.

You could plot this for yourself, but im going to do it in my head for simplicity. We also need to find the slope of this function in order for us to find the y-intercept. The slope is change in y divided by the change in x. Subtract the initial position from the final position.

3 - 1 = 2

0 - (-4) = 4

2/4 = 1/2

The new equation is:

$y=\frac{1}{2} x+b\\plugin(0,3)\\3=\frac{1}{2} (0)+b\\b=3$

Everything is shaded below and to the right of the line. They said the line was solid, so that means less than or equal to, $\leq$