Problem Analysis:
The task involves solving the equation \( 2x - 4 = 6 \) and understanding its graphical representation. Let's break it down step by step.
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Step 1: Solve the Equation Algebraically
The given equation is:
\[
2x - 4 = 6
\]
1. Add 4 to both sides of the equation to isolate the term with \( x \):
\[
2x - 4 + 4 = 6 + 4
\]
\[
2x = 10
\]
2. Divide both sides by 2 to solve for \( x \):
\[
x = \frac{10}{2}
\]
\[
x = 5
\]
So, the solution to the equation \( 2x - 4 = 6 \) is:
\[
x = 5
\]
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Step 2: Understand the Graphical Representation
The equation \( 2x - 4 = 6 \) can be rewritten in the form \( y = 2x - 4 \). This is a linear equation, and its graph is a straight line.
1.
Graph of \( y = 2x - 4 \):
- The slope of the line is 2 (since the coefficient of \( x \) is 2).
- The y-intercept is \(-4\) (since when \( x = 0 \), \( y = -4 \)).
2.
Finding the Point Where \( y = 6 \):
- We are asked to find the value of \( x \) when \( y = 6 \). This corresponds to the point where the line \( y = 2x - 4 \) intersects the horizontal line \( y = 6 \).
- From the algebraic solution, we know that when \( y = 6 \), \( x = 5 \). Therefore, the point of intersection is \( (5, 6) \).
3.
Verification on the Graph:
- The graph shows a straight line representing \( y = 2x - 4 \).
- The point \( (5, 6) \) is marked on the graph, confirming that when \( x = 5 \), \( y = 6 \).
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Step 3: Final Answer
The solution to the equation \( 2x - 4 = 6 \) is \( x = 5 \). This is verified both algebraically and graphically.
\[
\boxed{x = 5}
\]
Parent Tip: Review the logic above to help your child master the concept of graphing linear equations examples.
