Question

find an equation of the line that contains the points listed in the following table.

x	y
1	-3
2	-6
3	-9
4	-12

the equation of the line is y = \boxed{}.
(use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Identify slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's use \((0,0)\) and \((1, - 3)\).
\( m=\frac{-3 - 0}{1 - 0}=\frac{-3}{1}=-3 \).

Step2: Use slope - intercept form

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. From the point \((0,0)\), when \( x = 0 \), \( y=0 \). Substituting \( x = 0 \), \( y = 0 \) and \( m=-3 \) into \( y=mx + b \), we get \( 0=-3(0)+b \), so \( b = 0 \).

Step3: Write the equation

Substitute \( m=-3 \) and \( b = 0 \) into \( y=mx + b \), we get \( y=-3x+0 \), which simplifies to \( y=-3x \).

Answer:

\( y = - 3x \)