Question

The graph of a linear function contains the points (2,-6) and (8,3). What is the zero of the function?

Answer 1

B

Explanation:

the graph of a linear function has an equation of the form

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

calculate slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (2, - 6) and (x₂, y₂ ) = (8, 3) ← 2 points on the graph

substitute these values into the formula for m

m =
`(3-(-6))/(8-2)` =
`(3+6)/(6)` =
`(9)/(6)` =
`(3)/(2)` . then

y =
`(3)/(2)` x + c ← is the partial equation

to find c, substitute any of the 2 points into the partial equation

using (2, - 6 ) for x and y in the partial equation

- 6 =
`(3)/(2)` (2) + c = 3 + c ( subtract 3 from both sides )

- 9 = c

y =
`(3)/(2)` x - 9 ← equation of linear function

To find the zero, where the graph crosses the x- axis , let y = 0 and solve for x

0 =
`(3)/(2)` x - 9 ( add 9 to both sides )

9 =
`(3)/(2)` x ( multiply both sides by 2 )

18 = 3x ( divide both sides by 3 )

6 = x

That is the zero of the function is x = 6