Question

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

Answer 1

Answer:

The function that best represent the given graph is;

$y=\frac{3}{4}x-7$

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;

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

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

$\begin{gathered} y=mx+b \\ y=\frac{3}{4}x-7 \end{gathered}$

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

$y=\frac{3}{4}x-7$