Question

write the linear equation that gives the rule for this
x | y
-90 | -55
-46 | -11
-2 | 33
42 | 77
write your answer as an equation with y first, followed

Explanation:

Step1: Calculate the slope \( m \)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points, say \((-90, -55)\) and \((-46, -11)\).
\( m = \frac{-11 - (-55)}{-46 - (-90)} = \frac{-11 + 55}{-46 + 90} = \frac{44}{44} = 1 \)

Step2: Find the y-intercept \( b \)

Use the slope-intercept form \( y = mx + b \) and a point, e.g., \((-2, 33)\) with \( m = 1 \).
\( 33 = 1 \times (-2) + b \)
\( 33 = -2 + b \)
\( b = 33 + 2 = 35 \)

Step3: Write the linear equation

With \( m = 1 \) and \( b = 35 \), the equation is \( y = x + 35 \)

Answer:

\( y = x + 35 \)