Question

Which linear inequality is represented by the graph?

Answer 1

We must find the slope of the graph first, we can do this by finding two perfect points and inputting those points into the formula y2 - y1/x2 - x1

Perfect point #1: (0,1)

Perfect point #2: (2,5)

As mentioned above, input these numbers into our formula.

5-1 = 4

2 - 0 = 2

4/2 = 2

So, the slope of the graph is 2.

Now, we must find the y-intercept which can be found based on where the line intersects with the y-axis. As we can see, the line intersects at (0,1) therefore the y-intercept of the graph is 1.

We now form a linear equation:

y = 2x + 1

However, since this is linear equality graph we will replace the equal sign with an inequality symbol. The inequality symbol we can use is based on the direction of the shaded area. If shaded up, we use the "greater than symbol", if down then we use the "less than symbol".

The line also matters, if the line is dotted we use the normal inequality symbol, but if it is straight then we use one of the "equal to" inequality symbols.

As for our graph, we have a dotted line with the shaded area upwards. Therefore, we will be using the greater than symbol and not a "equal to" symbol.

So, our answer would be y > 2x + 1