To graph the two functions, let's break them down and plot them individually:

### 1. \( f(x) = x - 1 + 4 \)

This is a simplified linear equation. Combine like terms:

\[
f(x) = x + 3
\]

This represents a straight line with:
- **Slope (m) = 1**, meaning the line rises by 1 unit for every 1 unit it moves to the right.
- **Y-intercept (b) = 3**, meaning the line crosses the y-axis at \( (0, 3) \).

### 2. \( y = -3x + 7 \)

This is also a linear equation in slope-intercept form, \( y = mx + b \), where:
- **Slope (m) = -3**, meaning the line falls by 3 units for every 1 unit it moves to the right.
- **Y-intercept (b) = 7**, meaning the line crosses the y-axis at \( (0, 7) \).

### Plotting the Graphs

#### For \( f(x) = x + 3 \):
1. Start by plotting the y-intercept at \( (0, 3) \).
2. Use the slope \( 1 \), so move up 1 unit and right 1 unit from the y-intercept, and plot more points.
3. Connect the points with a straight line.

#### For \( y = -3x + 7 \):
1. Start by plotting the y-intercept at \( (0, 7) \).
2. Use the slope \( -3 \), so move down 3 units and right 1 unit from the y-intercept, and plot more points.
3. Connect the points with a straight line.

You should now have two lines on the graph: one with a positive slope and one with a negative slope. They will intersect at some point.

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Would you like to see a visual graph for these two lines or further clarifications?

### 5 Related Questions:
1. What is the intersection point of the two lines?
2. How does changing the slope affect the graph of a line?
3. Can you determine the x-intercept of both lines?
4. How can you solve for \( x \) when the two lines intersect?
5. How would the graph change if the constants (intercepts) were different?

**Tip:** Always look at the slope to quickly predict how steep or flat a line will be on a graph.

Learn how to graph the linear equations f(x) = x + 3 and y = -3x + 7. This tutorial covers key algebraic concepts such as slope, intercepts, and graphing straight lines, suitable for students in Grades 8-10.

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