Question

19 find the slope of the line that passes through all of the points on the table.
x | y
-2 | -7
0 | -8
2 | -9
4 | -10
6 | -11
show your work here
slope =
y - intercept =

Explanation:

Step1: Recall the 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 \((-2, -7)\) and \((0, -8)\).

Step2: Calculate the slope

Substitute \( x_1=-2,y_1 = -7,x_2=0,y_2=-8 \) into the slope formula:
\( m=\frac{-8-(-7)}{0 - (-2)}=\frac{-8 + 7}{0 + 2}=\frac{-1}{2}=-\frac{1}{2} \)
We can verify with another pair of points, say \((0, -8)\) and \((2, -9)\):
\( m=\frac{-9-(-8)}{2-0}=\frac{-9 + 8}{2}=\frac{-1}{2}=-\frac{1}{2} \)

Step3: Find the y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y=-8 \). So the y - intercept \( b=-8 \).

Answer:

slope \(=-\frac{1}{2}\)
y - intercept \(=-8\)