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.