Question

write the linear equation that gives the rule for this table.

x | y
1 | 12
2 | 24
3 | 36
4 | 48

write your answer as an equation with y first, followed by an equ

Explanation:

Step1: Find the slope (m)

The slope \( m \) of a line is calculated by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table, say \( (1, 12) \) and \( (2, 24) \). Then \( m=\frac{24 - 12}{2 - 1}=\frac{12}{1} = 12 \).

Step2: Find the y - intercept (b)

The equation of a line is \( y=mx + b \). We know \( m = 12 \), and we can use a point, for example, \( (1,12) \). Substitute \( x = 1 \), \( y = 12 \) and \( m=12 \) into \( y=mx + b \): \( 12=12\times1 + b \). Solving for \( b \), we get \( 12 = 12 + b \), so \( b=0 \).

Step3: Write the equation

Since \( m = 12 \) and \( b = 0 \), the equation of the line is \( y=12x+0 \), which simplifies to \( y = 12x \).

Answer:

\( y = 12x \)