Question

graph the line given by the equation below:

\\y + 2 = -3(x + 4)\\

Explanation:

⚡ Using what you learned: understanding linear functions

Step 1: Identify the point and slope

The given equation is in point-slope form:
\[ y - y_1 = m(x - x_1) \]

Comparing \( y + 2 = -3(x + 4) \) to the standard form:

• Slope \( m = -3 \)
• Point \( (x_1, y_1) = (-4, -2) \)

Step 2: Find a second point using the slope

Start at the point \( (-4, -2) \). Use the slope \( m = \frac{-3}{1} \) (down 3 units, right 1 unit):
\[ (-4 + 1, -2 - 3) = (-3, -5) \]

Alternatively, use \( m = \frac{3}{-1} \) (up 3 units, left 1 unit):
\[ (-4 - 1, -2 + 3) = (-5, 1) \]

Step 3: Graph the line

1. Plot the first point at \( (-4, -2) \).
2. Plot a second point at \( (-5, 1) \) or \( (-3, -5) \).
3. Draw a straight line passing through these points.

Answer:

To graph the line, plot the following two points on the coordinate plane and connect them with a straight line:

• Point 1: \( (-4, -2) \)
• Point 2: \( (-5, 1) \) (or \( (-3, -5) \))