Question

which steps should be used to graph the equation below?

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

\bigcirc 1. plot the point (2, 4).

1. from that point, count left 3 units and down 1 unit and plot a second point.
2. draw a line through the two points.

\bigcirc 1. plot the point (2, 4).

1. from that point, count left 1 unit and down 3 units and plot a second point.
2. draw a line through the two points.

\bigcirc 1. plot the point (-2,4).

1. from that point, count left 3 units and down 1 unit and plot a second point.
2. draw a line through the two points.

\bigcirc 1. plot the point (-2,4).

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 4=\frac{1}{3}(x + 2) \), which is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(- 2,4) \) and the slope \( m = \frac{1}{3}=\frac{\text{rise}}{\text{run}}=\frac{1}{3} \) (or we can also use the equivalent \( \frac{- 1}{-3} \)).

Step2: Analyze the first step of each option

• For the first option, the point plotted is \( (2,4) \), but from the point - slope form, the point should be \( (-2,4) \), so this option is incorrect.
• For the second option, the point plotted is \( (2,4) \), which is wrong as the correct point from the equation is \( (-2,4) \), so this option is incorrect.
• For the third option, the point plotted is \( (-2,4) \), which is correct. Now, let's check the slope. The slope \( m=\frac{1}{3} \), and if we consider the slope as \( \frac{-1}{-3} \) (since slope is also \( \frac{\text{change in }y}{\text{change in }x} \)), moving left 3 units (change in \( x=-3 \)) and down 1 unit (change in \( y = - 1 \)) gives a slope of \( \frac{-1}{-3}=\frac{1}{3} \), which is consistent with the slope of the line.
• (We can assume the fourth option, which is partially shown, would be incorrect based on the first three. But since the third option has the correct starting point and a correct way to use the slope)

Answer:

1. Plot the point \((-2,4)\).
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. (The option corresponding to these steps, which is the third option in the given choices)