Answer:
The rule is: y = -10x+85
Step-by-step explanation:
The rule is given by:
[tex]y = mx+b[/tex]
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:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Putting the values
[tex]m = \frac{65-75}{2-1}\\m = -10[/tex]
Putting the value of slope
[tex]y = -10x+b[/tex]
Putting a pair of input-output in the equation (1,75)
[tex]75 = -10(1) +b\\75 = -10+b\\b = 75+10\\b = 85[/tex]
Putting the value of b
[tex]y = -10x+85[/tex]
Hence,
The rule is: y = -10x+85
