Answer: The required slope-intercept form of the function is [tex]y=5x+3.[/tex]
Step-by-step explanation: We are given to find the slope-intercept form of the function described by the following table :
x 1 2 3 4
y 8 13 18 23
From the above table, we have the values
y(1) = 8, y(2) = 13, y(3) = 18 and y(4) = 23.
We know that the slope of a function passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, if we consider the points (1, 8) and (2, 13), then the slope of the given function will be
[tex]m=\dfrac{13-8}{2-1}\\\\\Rightarrow m=5.[/tex]
Since the function passes through the point (1, 8), so its equation is
[tex]y-8=m(x-1)\\\\\Rightarrow y=5(x-1)+8\\\\\Rightarrow y=5x+3.[/tex]
Thus, the required slope-intercept form of the function is
[tex]y=5x+3.[/tex]
We want to find the linear equation from the data in the given table.
Our line is: y = 5*x + 3
A general line can be written in slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So here we just need to use two of the points in the table.
We can use the first two:
(1, 8) and (2, 13).
The slope will be:
[tex]a = \frac{13 - 8}{2 - 1} = 5[/tex]
we get the line:
y = 5*x + b
To find the value of b, we can replace the values of one of the points in the equation, for example using the first point (1, 8) we get:
8 = 5*1 + b
8 - 5 = 3 = b
Finally, we can see that our equation is:
y = 5*x + 3
If you want to learn more, you can read:
https://brainly.com/question/10723900
