To graph the equation given by [tex]\( y - 4 = \frac{1}{3}(x + 2) \)[/tex], we can follow a series of steps. Here is a detailed, step-by-step solution to determine the correct procedure for plotting this equation:
1. Identify the Point-Slope Form:
The given equation [tex]\( y - 4 = \frac{1}{3}(x + 2) \)[/tex] 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.
Rewrite the equation in the form [tex]\( y - y_1 = m(x - x_1) \)[/tex]:
[tex]\[
y - 4 = \frac{1}{3}(x - (-2))
\][/tex]
So, the initial point [tex]\( (x_1, y_1) \)[/tex] is [tex]\( (-2, 4) \)[/tex] and the slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{3} \)[/tex].
2. Plot the Initial Point:
Plot the point [tex]\( (-2, 4) \)[/tex] on the coordinate plane. This is your starting point.
3. Use the Slope to Find the Next Point:
The slope [tex]\( m = \frac{1}{3} \)[/tex] means that for every 3 units you move to the right (increase in [tex]\( x \)[/tex]), you move 1 unit up (increase in [tex]\( y \)[/tex]). Alternatively, you can think of moving 3 units to the left (decrease in [tex]\( x \)[/tex]) and 1 unit down (decrease in [tex]\( y \)[/tex]) to plot a second point.
From the point [tex]\( (-2, 4) \)[/tex]:
- Move left 3 units, which takes [tex]\( x \)[/tex] from [tex]\(-2\)[/tex] to [tex]\(-5\)[/tex].
- Move down 1 unit, which takes [tex]\( y \)[/tex] from 4 to 3.
The next point is [tex]\( (-5, 3) \)[/tex].
4. Draw the Line:
Plot the second point [tex]\( (-5, 3) \)[/tex]. Draw a straight line through the points [tex]\( (-2, 4) \)[/tex] and [tex]\( (-5, 3) \)[/tex].
Given the steps outlined above, the correct step-by-step procedure to graph the equation provided 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.
Thus, the correct option 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.
