Answer:
y = x - 1
Step-by-step 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) = [tex] \frac{f(b) - f(a)}{b - a} [/tex],
Where,
b = 4
f(b) = 3
a = 3
f(a) = 2
Plug in the values
[tex] \frac{3 - 2}{4 - 3} = \frac{1}{1} [/tex]
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
