1. **State the problem:** We need to draw the graph of the linear function $y = 3x - 4$ on a Cartesian coordinate plane. 2. **Formula and explanation:** The function is given by the formula $y = 3x - 4$, where $3$ is the slope (rate of change) and $-4$ is the y-intercept (the point where the line crosses the y-axis). 3. **Calculate points:** To plot the graph, calculate $y$ for several values of $x$: - For $x = -2$: $$y = 3(-2) - 4 = -6 - 4 = -10$$ - For $x = -1$: $$y = 3(-1) - 4 = -3 - 4 = -7$$ - For $x = 0$: $$y = 3(0) - 4 = 0 - 4 = -4$$ - For $x = 1$: $$y = 3(1) - 4 = 3 - 4 = -1$$ - For $x = 2$: $$y = 3(2) - 4 = 6 - 4 = 2$$ 4. **Plot points:** The points to plot are $(-2, -10)$, $(-1, -7)$, $(0, -4)$, $(1, -1)$, and $(2, 2)$. 5. **Draw the line:** Connect these points with a straight line extending across the grid. This line represents the graph of $y = 3x - 4$. Final answer: The graph passes through the points calculated and has slope 3 and y-intercept -4.