Question

write the linear equation that gives the rule for this table.
x | y
8 | 44
16 | 60
24 | 76
32 | 92
write your answer as an equation with y first, followed by an equals sign.

Explanation:

Step1: Find the slope (m)

The formula for slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using the first two points (8, 44) and (16, 60):
\( m = \frac{60 - 44}{16 - 8} = \frac{16}{8} = 2 \)

Step2: Find the y-intercept (b)

Use the point-slope form \( y = mx + b \) and plug in \( m = 2 \) and a point (e.g., (8, 44)):
\( 44 = 2(8) + b \)
\( 44 = 16 + b \)
Subtract 16 from both sides: \( b = 44 - 16 = 28 \)

Step3: Write the equation

Using \( m = 2 \) and \( b = 28 \), the equation is \( y = 2x + 28 \)

Answer:

\( y = 2x + 28 \)