Question

1. (3, -4) and (6, -3) x1 y1 x2 y2 y = mx + b

Explanation:

Step1: Identify the two points

We have the points \((x_1, y_1) = (3, -4)\) and \((x_2, y_2) = (6, -3)\).

Step2: Calculate the slope \(m\)

The formula for slope \(m\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute the values: \(m=\frac{-3-(-4)}{6 - 3}=\frac{-3 + 4}{3}=\frac{1}{3}\).

Step3: Use point - slope form to find the equation

We use the point - slope form \(y - y_1=m(x - x_1)\). Let's use the point \((3,-4)\).
Substitute \(m = \frac{1}{3}\), \(x_1 = 3\) and \(y_1=-4\) into the formula:
\(y-(-4)=\frac{1}{3}(x - 3)\)
\(y + 4=\frac{1}{3}x-1\)
\(y=\frac{1}{3}x-1 - 4\)
\(y=\frac{1}{3}x-5\)

Answer:

The equation of the line is \(y=\frac{1}{3}x - 5\)