To graph the equation $y - 2 = 3(x - 7)$, we first need to rearrange it into slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step-by-step:

1. Start with the given equation: $y - 2 = 3(x - 7)$

2. Distribute the 3 on the right-hand side: $y - 2 = 3x - 21$

3. Add 2 to both sides to solve for $y$: $y = 3x - 21 + 2$ $y = 3x - 19$

Now the equation is in slope-intercept form: $y = 3x - 19$

Interpretation:

• The slope $m = 3$, meaning the line rises 3 units for every 1 unit it moves to the right.
• The y-intercept is $-19$, which means the line crosses the y-axis at $(0, -19)$.

Graph:

1. Start by plotting the y-intercept at $(0, -19)$.
2. From that point, use the slope $3$, which means go up 3 units and to the right 1 unit, to find more points.
3. Draw a straight line through these points.

Would you like a detailed graph or further explanation on this?

Here are five related questions to consider:

1. How do you find the x-intercept of the line?
2. What happens to the graph if the slope is changed to 5?
3. How does the equation change if the line is shifted up by 4 units?
4. How would the graph look if the slope was negative?
5. What is the difference between slope-intercept form and point-slope form?

Tip: When graphing lines, always check both the slope and the intercept carefully to plot the line accurately.