Q13. - Algebra 1

Question

Use the graph to determine the solution to the equation $-\frac{1}{3}x+1=0$?

Step-by-Step Solution

Answer

The solution to the equation $-\frac{1}{3}x+1=0$ is $x=3$.

Step 1. State the concept of linear equation.

A linear equation is the equation of a line. When you graph a linear equation, it's best to write the equation in slope-intercept form: 

$y=mx+c$

Remember that m is the slope of the line and b is the y-intercept (the y-coordinate of the point at which the line crosses the y-axis). 

Step 2. State the solution of linear equation graphically.

The solution of a linear equation (equation of line) are the points that lies on the line.

 

The points are the coordinates $\left(x,y\right)$ where x-coordinate is the value of x and y-coordinate is the value of y.

Step 3. Find the value of x .

Compare the equation $-\frac{1}{3}x+1=0$ with $y=mx+c$.

Observe the graph.

Notice the value of $y\left(y-\text{cordinate}\right)=0$

From the graph see that the $y-\text{cordinate}$ is 0 at $x=3$

Therefore the value of $x\left(x-\text{cordinate}\right)=3$.

Hence, $x=3$ is the solution of $-\frac{1}{3}x+1=0$.