Q14. - Algebra 1

Question

Solve each equation by graphing.

$14x-84=0$

Step-by-Step Solution

Answer

The solution of equation $14x-84=0$ is $x=6$.

Step 1. State the Concept of solving an equation by graphing.

A linear function is a function whose graph is a straight line. The solution or root of an equation is any value that makes the equation true. A linear equation has at most one root. Root of an equation can be calculated by graphing the related function. To write the related function for an equation, replace 0 with $f\left(x\right)$.

Step 2. Write the related function.

Since the equation is given to be , therefore, its related function will be .To graph the function, make a table.

 

x	$f\left(x\right)=14x-84$	$f\left(x\right)$	(x, $f\left(x\right)$)
6	$\begin{array}{c} f\left(6\right)=14\left(6\right)-84\\ =0\end{array}$	0	$\left(6,0\right)$
5	$\begin{array}{l}f\left(5\right)=14\left(5\right)-84\\ =-14\end{array}$	$-14$	$\left(5,-14\right)$

Step 3. Plot the function.

Graph the equation $14x-84=f\left(x\right)$ by plotting the values from the table and get:

The graph intersects the x-axis at 6. So, the solution is $x=6$.