How to Find x When y 5 Using the Equation y 4x - 3 and Its Graph

In this article, we will explore how to find the value of x when y 5 using both the equation y 4x - 3 and its graphical representation. We will guide you through the steps of using the equation to solve for x and show you how to find the intersection point on the graph.

Using the Equation to Solve for x

Given the equation y 4x - 3, we are asked to find the value of x when y 5.

Step 1: Set Up the Equation

Substitute y 5 into the equation:

5 4x - 3

Step 2: Solve for x

To solve for x, follow these steps:

Isolate the term with x on one side of the equation: Add 3 to both sides to move the constant to the right side: Divide both sides by 4 to isolate x:

Mathematically:

5 3 4x 8 4x 2 x

So, the value of x when y 5 is x 2.

Using the Graph to Find the Intersection Point

In addition to using the equation, you can also verify the solution by graphing both the line y 4x - 3 and the point (2, 5).

Step 1: Graph the line y 4x - 3.

Step 2: Plot the point (2, 5).

Step 3: Look for the intersection point of the line and the vertical line at x 2. The intersection point should be (2, 5).

Graphically, you can see that when x 2, the line y 4x - 3 intersects the point where y 5.

Additional Tips for Solving Linear Equations

Linear equations are fundamental in algebra and can be used to solve a variety of real-world problems. Here are a few additional tips to help you solve linear equations:

Check Your Work: Always double-check your work by substituting the values back into the original equation to ensure they are correct. Use Graphing Tools: Utilize graphing calculators or online graphing tools to visualize the equations and find intersection points more accurately. Practice Regularly: Regular practice will help you become more comfortable with solving linear equations and interpreting their graphical representations.

In conclusion, by using both the equation and the graph, you can effectively find the value of x when y 5 using the equation y 4x - 3.