Question

Determine the pattern rule for the table and write it as an equation.​

Answer 1

The rule is: y = -10x+85

Explanation:

The rule is given by:

`y = mx+b`

Here m is the gradient and b is the y-intercept.

We have to take two pairs of input-output to find the rule

Let the two pairs be:

(x1,y1) = (1,75)

(x2,y2) = (2,65)

Slope is found using the formula:

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

Putting the values

`m = (65-75)/(2-1)\\m = -10`

Putting the value of slope

`y = -10x+b`

Putting a pair of input-output in the equation (1,75)

`75 = -10(1) +b\\75 = -10+b\\b = 75+10\\b = 85`

Putting the value of b

`y = -10x+85`

Hence,

The rule is: y = -10x+85