Question

Solve the problem. Use what you learned from the model Graph the functions y = 2x + 1 and y = 24 -4 on the same grid to determine whether they are linear or non near Describe the similarities and differences between the graphs including their initial values and rates of change. Then graph the function y = 22 - 3 on the same grid. What are its similarities to the other two functions? Show your work. Use graphs, words, and numbers to explain your answer.

Answer 1

We have the functions

`\begin{gathered} y=2x+1 \\ \text{and} \\ y=2x-4 \end{gathered}`

if we graph the functions in the interval [0,5] we have

Now that we have the graphs we can se that they are linear, we also notice that they have the same rate of change (since they are parallel). The initial value of the function y=2x+1 is 1, whereas the initial value of the function y=2x-4 is -4. We also see that the slopes of each of the functions is 2. We can conclude all if we remember that a line written in the slope-intercept form is

`y=mx+b`

where m is the slope (or rate of change) and b is the intercept with the y-axis (the initial value in this case).

If we also graph the function y=2x-3 we have

We see that this function is also linear and that it has the same rate of change with the other two, whereas its initial value is -3.