Question

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

Answer 1

To graph the equation given in point-slope form, you can start by rewriting it in slope-intercept form (y = mx + b) if needed. The given equation is:

\[ y - 3 = \frac{1}{4}(x + 2) \]

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

2. Add 3 to both sides to isolate \(y\):
\[
y = \frac{1}{4}x + \frac{1}{2} + 3
\]
\[
y = \frac{1}{4}x + \frac{7}{2}
\]

Now, we can see the slope \(m = \frac{1}{4}\) and the y-intercept \(b = \frac{7}{2}\).

### Steps to Graph:

1. **Plot the y-intercept**: This is the point where the line crosses the y-axis, which is at \((0, \frac{7}{2})\) or \((0, 3.5)\).

2. **Use the slope**: From the y-intercept, use the slope of \(\frac{1}{4}\) to find another point on the line. This means for every 1 unit increase in \(y\), \(x\) increases by 4 units. Starting from \((0, 3.5)\), go up 1 unit in \(y\) (to 4.5) and right 4 units in \(x\) (to 4):

\[
(0 + 4, 3.5 + 1) \rightarrow (4, 4.5)
\]

3. **Plot another point**: You can also go down 1 unit in \(y\) (to 2.5) and left 4 units in \(x\) (to -4):

\[
(0 - 4, 3.5 - 1) \rightarrow (-4, 2.5)
\]

4. **Draw the line**: Connect the points \((0, 3.5)\), \((4, 4.5)\), and \((-4, 2.5)\) with a straight line extending in both directions.

Your line is complete! Now you can click on the graph to select the points and draw the line through them.