Question

Label the image correctly (some of the choices are wrong) : Is the graph increasing or decreasing?What is the slope?Does the line passes through the origin ?

Answer 1

Slope = - 3 / 2

Decreasing

It does not pass through the origin

Step-by-step explanation

We have the graph given.

First, let us find the slope of the graph. We do that with the formula:

`\text{m = }\frac{y2\text{ - y1}}{x2\text{ - x1}}`

where (x1, y1) and (x2, y2) are two points on the graph.

Let us pick points (-4, 2) and (4, -4)

So, we have that:

`\begin{gathered} m\text{ = }\frac{-4\text{ - 2}}{4\text{ - (-4)}}\text{= }\frac{-4\text{ - 2}}{4\text{ + 4}}\text{ = }(-6)/(8) \\ m\text{ = -}(3)/(2)\text{ or -1.5} \end{gathered}`

That is the slope.

When the slope of a graph is negative, it means that the graph is decreasing.

So, it is decreasing.

The origin of a cartesian plane is at point (0, 0).

The graph does not pass through this point, so it does not pass through the origin.