Question

Graph this line:
y–7=
–
1
2
(x–1)
Click to select points on the graph.

Answer 1

To graph the line given by the equation \( y - 7 = -\frac{1}{2}(x - 1) \), let's first rewrite the equation in slope-intercept form (y = mx + b).

Starting with:
\[ y - 7 = -\frac{1}{2}(x - 1) \]

Distributing \(-\frac{1}{2}\):
\[ y - 7 = -\frac{1}{2}x + \frac{1}{2} \]

Adding \(7\) to both sides:
\[ y = -\frac{1}{2}x + \frac{1}{2} + 7 \]
\[ y = -\frac{1}{2}x + 7.5 \]

Now we can see that the slope \(m\) is \(-\frac{1}{2}\) and the y-intercept \(b\) is \(7.5\).

### Steps to Graph the Line
1. **Plot the y-intercept (0, 7.5)**:
- This point is the starting point of your line on the y-axis.

2. **Use the slope to find another point**:
- The slope \(-\frac{1}{2}\) means that for every 2 units you move to the right (positive x-direction), you move down 1 unit (negative y-direction).
- From the point (0, 7.5), moving 2 units to the right brings you to (2, 7.5). Moving down 1 unit brings you to (2, 6.5).
- Now you have the point (2, 6.5).

3. **Plot the second point**:
- Plot the point (2, 6.5) on the graph.

4. **Draw the line**:
- Connect the points (0, 7.5) and (2, 6.5) with a straight line, extending it in both directions.

5. **(Optional) Find more points**:
- You can find more points by substituting different x-values into the original equation.

You can now click to select the points on the graph or plot them as discussed!