To graph the equation [tex]\( y - 4 = \frac{1}{3}(x + 2) \)[/tex], we can choose the correct steps as follows:
1. Understanding the Equation:
The equation is in point-slope form:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.
For this equation:
- The point [tex]\( (x_1, y_1) \)[/tex] is [tex]\( (-2, 4) \)[/tex].
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{3} \)[/tex].
2. Plot the First Point:
- Start by plotting the point [tex]\( (-2, 4) \)[/tex].
3. Using the Slope:
- The slope [tex]\( \frac{1}{3} \)[/tex] means that for every 3 units we move to the left in [tex]\( x \)[/tex], we move 1 unit down in [tex]\( y \)[/tex].
- From the point [tex]\( (-2, 4) \)[/tex], count 3 units to the left, which brings us to [tex]\( -2 - 3 = -5 \)[/tex] in [tex]\( x \)[/tex].
- Then move 1 unit down, which changes [tex]\( y \)[/tex] from 4 to [tex]\( 4 - 1 = 3 \)[/tex].
- The second point to plot is therefore [tex]\( (-5, 3) \)[/tex].
4. Plotting the Second Point:
- Plot the point [tex]\( (-5, 3) \)[/tex] on the graph.
5. Drawing the Line:
- Draw a line through the two points [tex]\( (-2, 4) \)[/tex] and [tex]\( (-5, 3) \)[/tex].
Thus, the correct steps are:
1. Plot the point [tex]\( (-2,4) \)[/tex].
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
So, the answer is:
```
1. Plot the point [tex]\( (-2,4) \)[/tex].
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
```
