Chapter 1, Problem 1RE

Sketching the Graph of an Equation In Exercises 1 and 2, construct a table of values that consists of several solution points of the equation. Use the resulting solution points to sketch the graph of the equation.

$y=-4x+1$

To determine

To graph: The equation $y=-4x+1$ by constructing a table of values which consists different solution points of the equation.

Explanation of Solution

Graph:

Consider the equation,

$y=-4x+1$

To find the different solution point, find the values of $y$ for different value of $x$.

For $x=-2$,

$\begin{array}{c}y=-4\left(-2\right)+1\\ =8+1\\ =9\end{array}$

The solution point is $\left(-2,9\right)$.

For $x=-1$,

$\begin{array}{c}y=-4\left(-1\right)+1\\ =4+1\\ =5\end{array}$

The solution point is $\left(-1,5\right)$.

For $x=0$,

$\begin{array}{c}y=-4\left(0\right)+1\\ =0+1\\ =1\end{array}$

The solution point is $\left(0,1\right)$.

For $x=1$,

$\begin{array}{c}y=-4\left(1\right)+1\\ =-4+1\\ =-3\end{array}$

The solution point is $\left(1,-3\right)$.

For $x=2$,

$\begin{array}{c}y=-4\left(2\right)+1\\ =-8+1\\ =-7\end{array}$

The solution point is $\left(2,-7\right)$.

The table given below shows the solution points of the equation $y=-4x+1$.

$\begin{array}{cccccc}x& -2& -1& 0& 1& 2\\ y& 9& 5& 1& -3& -7\\ \left(x,y\right)& \left(-2,9\right)& \left(-1,5\right)& \left(0,1\right)& \left(1,-3\right)& \left(2,-7\right)\end{array}$

Now, plot the points from the table and pass a line through them.

The figure given below shows the graph of the equation $y=-4x+1$.

From the graph, it can be observed that the equation forms a straight line and the solution points lie on the line.