Question

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

Explanation:

Step1: Identify the form

The equation \( y + 4 = -\frac{2}{3}(x - 2) \) is in the point - slope form of a linear equation, which is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope.

Step2: Analyze the components

• By comparing \( y + 4 = -\frac{2}{3}(x - 2) \) with \( y - y_1=m(x - x_1) \), we can rewrite \( y+4\) as \( y-(- 4) \).
• So, the slope \( m =-\frac{2}{3}\) and the point \( (x_1,y_1)=(2,-4) \) lies on the line.

If we want to convert it to slope - intercept form (\(y=mx + b\)):

Step3: Distribute the slope

First, distribute \( -\frac{2}{3} \) on the right - hand side: \( y+4=-\frac{2}{3}x+\frac{4}{3} \)

Step4: Solve for y

Subtract 4 from both sides. We know that \( 4=\frac{12}{3} \), so \( y=-\frac{2}{3}x+\frac{4}{3}-\frac{12}{3}=-\frac{2}{3}x-\frac{8}{3} \)

If the question was about identifying the slope and the point:

Answer:

The slope \( m =-\frac{2}{3}\) and the line passes through the point \( (2,-4) \)

If the question was about converting to slope - intercept form: