Graph the line with the equation \( y=3 x-3 \)

Sure, I can help you graph the linear equation \( y = 3x - 3 \). Here's a step-by-step guide to plotting this line: ### 1. Understand the Equation The equation \( y = 3x - 3 \) is in the slope-intercept form \( y = mx + b \), where: - **\( m \)** is the slope of the line. - **\( b \)** is the y-intercept (the point where the line crosses the y-axis). For \( y = 3x - 3 \): - **Slope (m)** = 3 - **Y-intercept (b)** = -3 ### 2. Plot the Y-Intercept Start by plotting the y-intercept on the coordinate plane. - **Point:** (0, -3)  ### 3. Use the Slope to Find Another Point The slope \( m = 3 \) can be interpreted as "rise over run." This means: - **Rise (Δy):** 3 units up - **Run (Δx):** 1 unit to the right From the y-intercept (0, -3): - Move **1 unit to the right**: New x-coordinate = 0 + 1 = 1 - Move **3 units up**: New y-coordinate = -3 + 3 = 0 - **Point:** (1, 0)  ### 4. Plot the Second Point Plot the second point on the graph. - **Point:** (1, 0) ### 5. Draw the Line Connect the two points with a straight line, and extend it in both directions. This line represents the equation \( y = 3x - 3 \).  ### 6. Additional Points (Optional) To ensure accuracy, you can plot additional points by choosing different values for \( x \) and solving for \( y \). | \( x \) | \( y = 3x - 3 \) | |---------|------------------| | -1 | \( y = 3(-1) - 3 = -6 \) → (-1, -6) | | 2 | \( y = 3(2) - 3 = 3 \) → (2, 3) | | 3 | \( y = 3(3) - 3 = 6 \) → (3, 6) | Plot these points and ensure they all lie on the line you've drawn. ### Final Graph Here is a visual representation of the graph: ``` y | 6| * 5| 4| 3| * 2| 1| 0|--------*--------- -1| -2| -3|* -4| -5| -6| --------------------- x -2 -1 0 1 2 3 ``` - **(0, -3)** and **(1, 0)** are plotted, and the line extends through these points. - Additional points like **(-1, -6)**, **(2, 3)**, and **(3, 6)** also lie on the line. ### Summary - **Slope (3):** For every 1 unit increase in \( x \), \( y \) increases by 3 units. - **Y-Intercept (-3):** The line crosses the y-axis at (0, -3). - **Linearity:** The graph is a straight line since the equation is linear. Feel free to use graphing software or graph paper to plot the points accurately and draw the line. If you have any more questions or need further assistance, let me know!