Question

write the linear equation that gives the rule for this table.
x | y
1 | 21
2 | 42
3 | 63
4 | 84
write your answer as an equation with y first, followed by an equals sign.
submit

Explanation:

Step1: Find the slope (m)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the first two points \((1, 21)\) and \((2, 42)\). Then \( m=\frac{42 - 21}{2 - 1}=\frac{21}{1} = 21 \).

Step2: Find the y - intercept (b)

The equation of a line is \( y=mx + b \). We know \( m = 21 \) and we can use the point \((1,21)\). Substitute \( x = 1 \), \( y = 21 \) and \( m=21 \) into the equation: \( 21=21\times1 + b \). Simplifying, \( 21 = 21 + b \), so \( b=0 \).

Step3: Write the equation

Using \( y=mx + b \) with \( m = 21 \) and \( b = 0 \), the equation is \( y = 21x \).

Answer:

\( y = 21x \)