Question

What is the slope of the table? what is the equation ot the table?

Answer 1

A linear equation in the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Given two points (x₁, y₁) and (x₂, y₂), the slope (m) can be calculated:

`m=(y_2-y_1)/(x_2-x_1)`

So, to find the slope and the equation of the line, follow the steps below.

Step 01: Choose two points from the table and calculate "m".

Let's choose the points (0, 8) and (2, 14).

Substituting them in the equation:

`\begin{gathered} m=(14-8)/(2-0) \\ m=(6)/(2) \\ m=3 \end{gathered}`

The slope is 3.

Step 02: Choose one point and substitute in the equation of the line to find b.

Knowing that m = 3, the equation of the line is:

`y=3x+b`

Choosing the point (0, 8) and substituting it in the equation:

`\begin{gathered} 8=3\cdot0+b \\ 8=0+b \\ 8=b \end{gathered}`

So, the equation is:

`y=3x+8`

Answer:

The slope is 3.

The equation of the line is y = 3x + 8.