Question

Which function is best represented by the graph at the right?

Answer 1

The function that best represent the given graph is;

`y=(3)/(4)x-7`

Step-by-step explanation:

We want to find the function that best represent the given graph.

Recall that the slope-intercept form of linear equation can be written as;

`y=mx+b`

where;

`\begin{gathered} m=\text{slope} \\ b=\text{intercept on the y-axis} \end{gathered}`

From the given graph, the intercept on the y axis is at;

`\begin{gathered} \text{ point (0,-7)} \\ b=-7 \end{gathered}`

We need to find the slope.

Using two points on the graph;

`\begin{gathered} (0,-7) \\ \text{and} \\ (8,-1) \end{gathered}`

The slope is;

`\begin{gathered} m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{substituting the coordinates;} \\ m=\frac{-1-(-7)_{}}{8-0}=(-1+7)/(8) \\ m=(6)/(8) \\ m=(3)/(4) \end{gathered}`

Since we have the slope and the intercept, we can now write the equation of the line;

`\begin{gathered} y=mx+b \\ y=(3)/(4)x-7 \end{gathered}`

Therefore, The function that best represent the given graph is;

`y=(3)/(4)x-7`