Question

This graph shows how the total number of vocal pieces Will can sing depends on the numberof weeks he takes voice lessons. The variable w represents the number of weeks he hastaken voice lessons, and the variable p represents the total number of pieces he has learned.Vocal pieces will can sing10090807060Number of pieces learned504030201060708090+10010 20 30

Answer 1

The general form of a linear equation is:

$y=mx+b$

Where m is the slope, represented by:

$m=\frac{change\text{ in x}}{\text{change in y}}$

And b is the intercept with the y-axis.

We can find the slope and the intercept with the y-axis by looking at the graph we are given. We can see that in the graph the x-axis is represented with the letter w (number of weeks) and y-axis is represented with the letter p (number of pieces he has learned).

We would have a linear equation similar to this:

$p=mw+b$

From looking at the graph, we can identify that the intercept with the p-axis is 30.

$b=30$

And to find the slope, we can take two pair of points from the line in the graph:

$m=\frac{p_1-p_2}{w_1-w_2}$

I am going to take points (30, 50) and (60,70)

$m=\frac{50-70}{30-60}=\frac{2}{3}$

The equation for the relationship shown in the graph is:

$p=\frac{2}{3}w+30$