Question

Graph this line:
y–3=
1
4
(x+2)
Click to select points on the graph.

Answer 1

To graph the line represented by the equation \( y - 3 = \frac{1}{4}(x + 2) \), we can first rewrite it in slope-intercept form, which is \( y = mx + b \).

1. Start with the equation given:
\[
y - 3 = \frac{1}{4}(x + 2)
\]

2. Distribute the \(\frac{1}{4}\) on the right side:
\[
y - 3 = \frac{1}{4}x + \frac{1}{2}
\]

3. Add 3 to both sides to isolate \(y\):
\[
y = \frac{1}{4}x + \frac{1}{2} + 3
\]
Convert 3 to a fraction with a denominator of 2:
\[
3 = \frac{6}{2}
\]
So,
\[
y = \frac{1}{4}x + \frac{1}{2} + \frac{6}{2} = \frac{1}{4}x + \frac{7}{2}
\]

Now we have the slope-intercept form:
\[
y = \frac{1}{4}x + \frac{7}{2}
\]

### Identifying Points to Graph:

You can find points on this line by choosing values for \(x\) and calculating the corresponding \(y\).

**For example:**
- When \(x = -2\):
\[
y = \frac{1}{4}(-2) + \frac{7}{2} = -\frac{1}{2} + \frac{7}{2} = \frac{6}{2} = 3
\]
Point: \((-2, 3)\)

- When \(x = 0\):
\[
y = \frac{1}{4}(0) + \frac{7}{2} = \frac{7}{2} = 3.5
\]
Point: \((0, 3.5)\)

- When \(x = 2\):
\[
y = \frac{1}{4}(2) + \frac{7}{2} = \frac{1}{2} + \frac{7}{2} = \frac{8}{2} = 4
\]
Point: \((2, 4)\)

### Graphing the Line:

1. Plot the points \((-2, 3)\), \((0, 3.5)\), and \((2, 4)\) on a coordinate plane.
2. Draw a straight line through these points, extending it in both directions.

### Summary of Points to Use:
- \((-2, 3)\)
- \((0, 3.5)\)
- \((2, 4)\)

This line has a slope of \(\frac{1}{4}\) (which means it rises 1 unit for every 4 units it runs to the right) and a \(y\)-intercept of \(\frac{7}{2}\) or \(3.5\).