To graph the equation [tex]\( y - 4 = \frac{1}{3}(x + 2) \)[/tex], we should use the following steps:
1. Plot the point [tex]\((-2,4)\)[/tex]:
- The given equation is in the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is the point on the line and [tex]\( m \)[/tex] is the slope.
- From the equation, we observe that it crosses the point [tex]\((-2, 4)\)[/tex].
2. From that point, count left 3 units and down 1 unit and plot a second point:
- The slope of the line is [tex]\(\frac{1}{3}\)[/tex], which indicates that for every 3 units moved horizontally to the left, the vertical movement should be 1 unit downwards.
- Starting from [tex]\((-2, 4)\)[/tex], we move 3 units to the left and 1 unit down, reaching the point [tex]\((-5, 3)\)[/tex].
3. Draw a line through the two points:
- Now, simply draw a straight line connecting the points [tex]\((-2, 4)\)[/tex] and [tex]\((-5, 3)\)[/tex], which will represent the graph of the equation.
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.
