Question

Find the equation of the linear function represented by the table below in slope-

Answer 1

The picture attached has the table that repfesents the linear function to find the equation.

Answer:

• y = 10x - 6

Explanation:

A linear function 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, slope-intercept 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.