Question

Determine the slope and y intercept from table Math HW

Answer 1

Answer:

slope = -1

y-intercept = 6

Step-by-step 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

`\begin{gathered} slope\text{ = }\frac{change\text{ in y}}{change\text{ in x}} \\ \\ slope\text{ = }(3-5)/(3-1)\text{ = }(-2)/(2)=-1 \\ slope\text{ = }(0-3)/(6-3)\text{ = }(-3)/(3)\text{ = -1} \\ slope\text{ = }(-2-0)/(8-6)\text{ = }(-2)/(2)\text{ = -1} \end{gathered}`

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:

`\begin{gathered} \text{y = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}`

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

`\begin{gathered} 0\text{ = -1\lparen6\rparen + b} \\ 0\text{ = -6 + b} \\ b\text{ = 6} \end{gathered}`

Hence, the y-intercept is 6