A linear function is given. Complete parts​ (a)-(d).
f left parenthesis x right parenthesis equals negative 3 x plus 4
Use the slope and​ y-intercept to graph the linear function.

Given the linear function:

\[
f(x) = -3x + 4
\]

This is in slope-intercept form, \( y = mx + b \), where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

### (a) Identify the slope and y-intercept:
- **Slope (m)**: The slope is \( -3 \), meaning for every unit increase in \( x \), \( y \) decreases by 3 units.
- **Y-intercept (b)**: The y-intercept is \( 4 \), meaning the graph crosses the y-axis at \( (0, 4) \).

### (b) Plot the y-intercept:
- Start by plotting the point \( (0, 4) \) on the coordinate plane.

### (c) Use the slope to find another point:
- From the point \( (0, 4) \), use the slope \( -3 \). 
  - The slope \( -3 \) can be interpreted as \( -3/1 \). So, from \( (0, 4) \), move 1 unit to the right and 3 units down to get the next point:
  - New point: \( (1, 1) \).

### (d) Graph the line:
- Plot the points \( (0, 4) \) and \( (1, 1) \).
- Draw a straight line through these two points to represent the linear function.

Would you like a visual graph or more details on how to plot this manually?

### Related Questions:
1. What does the slope \( -3 \) indicate about the steepness of the line?
2. How does the y-intercept influence where the line crosses the y-axis?
3. What is the x-intercept of the function \( f(x) = -3x + 4 \)?
4. How would the graph change if the slope were positive?
5. What happens to the graph if the y-intercept decreases?

### Tip:
Remember, the slope tells you how steep the line is and in which direction it tilts. Positive slopes rise, while negative slopes fall.

A linear function is given. Complete parts​ (a)-(d). f(x) = -3x + 4. Use the slope and​ y-intercept to graph the linear function.

Learn how to graph the linear function f(x) = -3x + 4 by identifying the slope and y-intercept. This step-by-step solution includes using the slope-intercept form and plotting points on the graph. Suitable for students in Grades 8-10.

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