Question

Which of the following equations describes the graph shown?

A.) y = x+2

B.) y = -x - 2

C.) y = x - 2

D.) y = -x + 2

Answer 1

Answer: The correct option is (D) y = -x + 2.

Step-by-step explanation: We are to select the correct equation that describes the given graph.

We can see that the graph is a straight line passing through the points (0, 2) and (1, 1).

So, the slope of the line will be

`m=(2-1)/(0-1)=-1.`

Therefore, the equation of the line with slope m = -1 and passing through the point (0, 2) is given by

`y-2=m(x-0)\\\\\Rightarrow y-2=-1* x\\\\\Rightarrow y-2=-x\\\\\Rightarrow y=-x+2.`

Hence, the equation that describes the graph is y = -x + 2.

Thus, (D) is the correct option.

Answer 2

By looking at the slant at which the line is going, you can tell if the line is negative or positive. This line is negative, so that removes two of the choices. By looking at where the line intersects the y-axis determines if its negative or positive. So the answer is D