Question

Fill in the missing number to complete the linear equation that gives the rule for this table. Explain/show how you got your answer in

as much detail as you can.

Answer 1

y = x - 1

Explanation:

To create a linear equation in the slope-intercept form, which is in the form of y = mx + b, we need to find the slope/rate of change, m, and the y-intercept, b.

Rate of change can be calculated using two pairs, (3, 2) and (4, 3)

Rate of change/slope (m) =
`(f(b) - f(a))/(b - a)`,

Where,

b = 4

f(b) = 3

a = 3

f(a) = 2

Plug in the values

`(3 - 2)/(4 - 3) = (1)/(1)`

m = 1

Plug in x = 3, y = 2 and m = 1 into y = mx + b

2 = 1(3) + b

Solve for b

2 = 3 + b

Subtract 3 from each side

2 - 3 = b

-1 = b

b = -1

Substitute m = 1 and b = -1 into y = mx + b.

y = 1(x) +(-1)

y = x - 1

The linear equation that gives the rule for this table is y = x - 1