Question

find the slope of the line that passes through all of the points on the table.
show your work here
slope =
y - intercept =

Explanation:

Step1: Recall slope formula

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 two points from the table, say \((-2, 2)\) and \((0, 20)\).

Step2: Substitute values into formula

Here, \( x_1=-2 \), \( y_1 = 2 \), \( x_2=0 \), \( y_2 = 20 \). So \( m=\frac{20 - 2}{0-(-2)}=\frac{18}{2}=9 \). We can check with another pair, like \((0, 20)\) and \((2, 38)\): \( m=\frac{38 - 20}{2 - 0}=\frac{18}{2}=9 \), confirming the slope.

Step3: Find y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 20 \), so the y - intercept is 20.

Answer:

slope \( = 9 \)
y - intercept \( = 20 \)