Graph y minus 2 equals 3 left parenthesis x minus 7 right parenthesisy−2=3(x−7).


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.

Learn how to graph the linear equation y - 2 = 3(x - 7) by converting it into slope-intercept form. This step-by-step solution includes detailed explanations on finding the slope, y-intercept, and graphing the equation. Suitable for Grades 8-10, covering algebraic concepts such as linear equations and graphing.

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