Question

Which equation can be used to represent the relationship between x and y for the points shown above?

Answer 1

`y=-(1)/(3)x+4`

Step-by-step explanation

We want to find the equation that represents the relationship between x and y.

The graph is a straight line graph.

The general form of a linear equation is given as:

y = mx + c

where m = slope

c = y intercept

First, we have to find the slope of the line. To do that, we apply the formula:

`m=(y2-y1)/(x2-x1)`

where (x1, y1) and (x2, y2) are two points that lie on the line.

Let us pick the points: (-3, 5) and (3, 3)

Therefore:

`\begin{gathered} m=(3-5)/(3-(-3))=(3-5)/(3+3)=(-2)/(6) \\ m=-(1)/(3) \end{gathered}`

From the graph, we can find the y intercept. It is the point where the graph touches the y axis.

The y intercept is 4.

Therefore, the equation of the line is:

`y=-(1)/(3)x+4`

That is the equatinon.