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The picture attached has the table that repfesents the linear function to find the equation.
Answer:
- y = 10x - 6
Explanation:
A<em> linear function</em> is characterized by a constant slope and a unique y-intercept.
Let m be the slope and b the y-intercept of a linear function. Then, s<em>lope-intercept</em> equation has the form:
- y = mx + b.
Using any two pair of points (x,y) from the table you can determine the values of m and b.
The table is:
x 0 1 2 3 4
y -6 4 14 24 34
You know that it is a linear function because for constant increases of the x-values (1 unit in the table) there is a constant increase of the y-values (10 in the table).
The slope, m, is calculated as:
- m = [change in y] / [change in x] = Δy / Δx = [14 - 4] [2 - 1] = 10
As said, you could have used any two points to calculate m,
The y-intercept, b, is the value of the function, y, when x = 0.
- From the table you can observe that when x = 0, the value of y is - 6; so b = - 6.
Thus, the equation of the linear function represented in the table in slope-intercept form is:
- y = 10x - 6.
