Answer:
The linear equation that gives the rule for this table will be:
Step-by-step explanation:
Taking two points from the table
Finding the slope between two points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(2,\:27\right),\:\left(x_2,\:y_2\right)=\left(3,\:28\right)[/tex]
[tex]m=\frac{28-27}{3-2}[/tex]
[tex]m=1[/tex]
We know the slope-intercept form of linear equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
substituting the point (2, 27) and m=1 in the slope-intercept form to determine the y-intercept 'b'
[tex]y=mx+b[/tex]
27 = 1(2)+b
27-2 = b
b = 25
Now, substituting m=1 and b=25 in the slope-intercept form to determine the linear equation
y=mx+b
y=1(x)+25
y=x+25
Thus, the linear equation that gives the rule for this table will be:
The linear equation that gives the rule of the table is f(x) = x + 25
The linear equation can be represented in a slope intercept form as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
Using the table let get 2 points
(2, 27)(3, 28)
let find the slope
m = 28 - 27 / 3 -2 = 1
let's find b using (2, 27)
27 = 2 + b
b = 25
Therefore,
y = x + 25
f(x) = x + 25
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