Answer:
slope = -1
y-intercept = 6
Explanation:
Given:
A table with x and y values
To find:
The slope and the y-intercept
To determine the slope of the values, we will calculate the change in y over the change in x
[tex]\begin{gathered} slope\text{ = }\frac{change\text{ in y}}{change\text{ in x}} \\ \\ slope\text{ = }\frac{3-5}{3-1}\text{ = }\frac{-2}{2}=-1 \\ slope\text{ = }\frac{0-3}{6-3}\text{ = }\frac{-3}{3}\text{ = -1} \\ slope\text{ = }\frac{-2-0}{8-6}\text{ = }\frac{-2}{2}\text{ = -1} \end{gathered}[/tex]
The slope is constant. The slope is -1
The y-intercept is the value of y when x = 0
To get the y-intercept from the table, we will check for the value of y when x = 0
We only have value for x when y = 0
We will use the linear equation:
[tex]\begin{gathered} \text{y = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]
using any point on the table and the slope, we will substitute in the formul to get b
let the point (x, y) = (6, 0), m = -1
[tex]\begin{gathered} 0\text{ = -1\lparen6\rparen + b} \\ 0\text{ = -6 + b} \\ b\text{ = 6} \end{gathered}[/tex]
Hence, the y-intercept is 6
