Use crossing graphs to solve problem. Round to nearest decimal point.

To solve a problem using crossing graphs, follow these steps:

### Steps for Graphical Solutions (Crossing Graphs):

1. **Write both equations** that you want to solve or compare.
2. **Graph both equations** on the same set of axes (use a graphing tool or manually plot points).
3. **Find the point where the graphs intersect**. The x-coordinate of the intersection is the solution to the equation.
4. **Round the result** to the nearest decimal point as required.

### Example Problem:
Solve \( f(x) = g(x) \) graphically. Suppose:
- \( f(x) = 2x + 3 \)
- \( g(x) = -x + 5 \)

#### Steps:
1. **Graph the equations**:
   - Plot \( f(x) = 2x + 3 \), which is a straight line with a slope of 2 and a y-intercept of 3.
   - Plot \( g(x) = -x + 5 \), which is a straight line with a slope of -1 and a y-intercept of 5.
   
2. **Find the intersection**: The two lines intersect at a point.

3. **Use a graphing tool or manual plot**: 
   Let's calculate using algebra to ensure precision. Set the two equations equal:
   \[
   2x + 3 = -x + 5
   \]
   Solve for \( x \):
   \[
   3x = 2 \quad \Rightarrow \quad x = \frac{2}{3} \approx 0.67
   \]
   
4. The solution is \( x = 0.7 \) after rounding to the nearest decimal.

5. **Verify the solution by substituting** \( x = 0.7 \) back into both equations:
   - For \( f(x) = 2(0.7) + 3 = 4.4 \)
   - For \( g(x) = -(0.7) + 5 = 4.3 \)

Since the graphs closely intersect around this value, we round the answer as \( x = 0.7 \).

Do you have a specific set of equations you'd like to solve with crossing graphs? Or would you like further explanation?

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### 5 Related Questions:
1. How do you plot a linear equation manually on graph paper?
2. What is the geometric interpretation of solving systems of equations?
3. How do different types of functions (e.g., quadratic, exponential) behave when graphed?
4. How can graphing tools or calculators be used to find intersections more accurately?
5. What are some real-world applications of finding the intersection of two graphs?

### Tip:
Using graphing software (like Desmos or GeoGebra) can make finding intersections much faster and more accurate.

Use crossing graphs to solve the problem. Round to the nearest decimal point.

Learn how to solve linear equations using crossing graphs and find the point of intersection. This guide covers the key concepts of graphical solutions and linear equations, with a step-by-step example. Perfect for students in Grades 9-11.

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