Question

5
(-3,0) and (-2,-1)
x₁y₁ x₂y₂
y = mx + b
(3, 4) and (6, -3)

Explanation:

Step1: Calculate the slope (m)

The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Given \((x_1, y_1)=(-3, 0)\) and \((x_2, y_2)=(-2, -1)\), substitute into the formula:
\( m = \frac{-1 - 0}{-2 - (-3)} = \frac{-1}{1} = -1 \).

Step2: Find the y-intercept (b)

Use the point-slope form \( y = mx + b \) and substitute one of the points (e.g., \((-3, 0)\)) and \( m = -1 \):
\( 0 = -1(-3) + b \)
\( 0 = 3 + b \)
Subtract 3 from both sides: \( b = -3 \).

Step3: Write the equation

Substitute \( m = -1 \) and \( b = -3 \) into \( y = mx + b \):
\( y = -x - 3 \).

Answer:

The equation of the line is \( y = -x - 3 \)