Question

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

x 0 1 2 3 4
y 7 15 23 31 39

Answer 1

y = 8x + 7

Explanation:

the equation of a linear function in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`\frac{y_{2-y_(1) } }{x_(2)-x_(1) }`

with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table

m =
`(23-15)/(2-1)` =
`(8)/(1)` = 8

the ordered pair (0, 7 ) indicates c = 7

y = 8x + 7 ← equation of linear function

Answer 2

y = 8x+7

Explanation:

firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....

Secondly, identify the common difference: 8
we now know that the answer must contain 8x

Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y