Question

The coordinates of three points on a straight line are listed in the table. What is the function rule that describes the linear relationship between these x and y values?

Answer 1

y = x - 8

Explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (10, 2) and (x₂, y₂ ) = (12, 4) ← 2 ordered pairs from the table

m =
`(4-2)/(12-10)` =
`(2)/(2)` = 1

From the graph the line crosses the y- axis at - 8 ⇒ c = - 8

y = x - 8 ← is the equation