Chapter 4.2, Problem 35E

To determine

To describe: two ways to graph the equation

Answer to Problem 35E

The two ways graph equation was drawn.

Explanation of Solution

Given:

  $y-1=\frac{3}{2}\left(x-4\right)$

Calculation:

Consider the equation $y-1=\frac{3}{2}\left(x-4\right)$

One way to graph the equation is the two point form

So, compare the equation with the slope-point form, the one point coordinates is $\left(4,1\right)$

Now, put value $x=0$ in the equation and find the value for y

  $\begin{array}{l}y-1=\frac{3}{2}\left(0-4\right)\\ y-1=-6\end{array}$

Take the constant on one side

  $\begin{array}{l}y=-6+1\hfill \\ =-5\hfill \end{array}$

Thus, the second point coordinates are $\left(0,-5\right)$

Now, draw the graph using the two pints $\left(0,-5\right)$ and $\left(4,1\right)$

  

Second way to draw the graph is putting the different values for x in the equation and finds the corresponding value for the variable y

So, the find the data set for the equation and make the table

x	0	1	2	3	4
y	-5	$-\frac{7}{2}$	-2	$-\frac{1}{2}$	1

Now, draw the graph using data set

  

Conclusion:

Therefore, the two ways graph equation was drawn.