Question

Use the slope and y-intercept to graph the equation.
Y = -5/3x + 4

Answer 1

To graph the equation \( y = -\frac{5}{3}x + 4 \), we'll start by identifying the slope and the y-intercept.

1. **Identify the slope and y-intercept**:
- The slope \( m \) is \(-\frac{5}{3}\).
- The y-intercept \( b \) is \( 4 \).

2. **Plot the y-intercept**:
- The y-intercept is the point where the line crosses the y-axis. This occurs when \( x = 0 \).
- So, plot the point \((0, 4)\) on the graph.

3. **Use the slope to find another point**:
- The slope \(-\frac{5}{3}\) means that for every 3 units you move to the right (in the positive x direction), you move down 5 units (in the negative y direction).
- From the y-intercept \((0, 4)\), move 3 units to the right to \( (3, 4) \), and then move down 5 units to reach the point \( (3, -1) \).
- So, plot the point \((3, -1)\).

4. **Draw the line**:
- Now that you have at least two points \((0, 4)\) and \((3, -1)\), you can draw a straight line through these points. Extend the line in both directions.

5. **Label the graph**:
- It's helpful to label the equation of the line and mark the slope and intercept for clarity.

Your graph will show a line that slopes downward from left to right, crossing the y-axis at 4 and continuing downward with a slope of \(-\frac{5}{3}\).