Question

Could the table represent a linear function give a formula if it could

Answer 1

Explanation:

We know that a linear function has the following form:

`\begin{gathered} y=mx+b \\ \text{m is the slope and b is the y-intercetp} \end{gathered}`

The slope is calculated as follows:

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

(a)

The slope at a, we calculate it with the points (0, 200) and (25, 100), replacing:

`m=(100-200)/(25-0)=(-100)/(25)=-4`

We know that the y-intercept (b) is equal to 200 because it is when x is equal to 0, therefore the equation would be:

`y=-4x+200`

(b)

The slope at b, we calculate it with the points (0, 200) and (35, 100), replacing:

`m=(100-200)/(25-0)=(-100)/(25)=-4`

We know that the y-intercept (b) is equal to 200 because it is when x is equal to 0, therefore the equation would be:

`y=-4x+200`