Question

question
what is an equation of the line that passes through the points (3, 6) and (1, -2)?
answer attempt 1 out of 2

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Given points \((3, 6)\) and \((1, -2)\), so \(x_1 = 3\), \(y_1 = 6\), \(x_2 = 1\), \(y_2=-2\).
\(m=\frac{-2 - 6}{1 - 3}=\frac{-8}{-2}=4\)

Step2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Let's use the point \((3, 6)\) (we could also use \((1,-2)\)).
Substitute \(m = 4\), \(x_1=3\), \(y_1 = 6\) into the formula:
\(y - 6=4(x - 3)\)
Expand the right - hand side: \(y-6 = 4x-12\)
Add 6 to both sides: \(y=4x-12 + 6\)
\(y=4x-6\)

Answer:

\(y = 4x-6\) (or in standard form \(4x-y=6\))