To graph the equation $y = 3x - 4$ for values of $x$ from -2 to 2, we need to first calculate the corresponding $y$-values for each $x$-value.

Step-by-step calculation of points:

For $x = -2$: $y = 3(-2) - 4 = -6 - 4 = -10$

For $x = -1$: $y = 3(-1) - 4 = -3 - 4 = -7$

For $x = 0$: $y = 3(0) - 4 = -4$

For $x = 1$: $y = 3(1) - 4 = 3 - 4 = -1$

For $x = 2$: $y = 3(2) - 4 = 6 - 4 = 2$

Points to plot:

• $(-2, -10)$
• $(-1, -7)$
• $(0, -4)$
• $(1, -1)$
• $(2, 2)$

These points form a straight line because the equation is linear. You can plot these points on a grid and draw a line through them to complete the graph.

Would you like me to generate the graph for you? Let me know if you have any questions or want further details!

Related questions:

1. How would the graph change if the slope was steeper, say $y = 5x - 4$?
2. What would happen to the graph if the constant term changes, e.g., $y = 3x - 6$?
3. Can you explain why the line is straight for linear equations?
4. What is the meaning of the slope 3 in $y = 3x - 4$?
5. How would you find the x-intercept of this line?

Tip:

When graphing linear equations, always calculate several points by substituting values of $x$, and remember, the slope determines how steep the line is!