Question

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

Answer 1

Answer:

The rule is: y = -10x+85

Step-by-step 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:

$m = \frac{y_2-y_1}{x_2-x_1}$

Putting the values

$m = \frac{65-75}{2-1}\\m = -10$

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