Q13. - Algebra 1

Question

Solve each equation by graphing.

$-5x+35=0$

Step-by-Step Solution

Answer

The solution of equation $-5x+35=0$ is $x=7$.

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 $-5x+35=0$, therefore, its related function will be $-5x+35=f\left(x\right)$. To graph the function, make a table.

 

x	$f\left(x\right)=-5x+35$	$f\left(x\right)$	(x, $f\left(x\right)$)
7	$\begin{array}{c}f\left(7\right)=-5\left(7\right)+35\\ =0\end{array}$	0	$\left(7,0\right)$
5	$\begin{array}{c}f\left(5\right)=-5\left(5\right)+35\\ =10\end{array}$	10	$\left(5,10\right)$

 

Step 3. Plot the function.

Graph the equation $-5x+35=f\left(x\right)$ by plotting the values from the table and get:

The graph intersects the x-axis at 7. So, the solution is $x=7$.