Question

Use the graph to write a linear function that relates y to x.

Answer 1

y =
`(1)/(3)` x + 3

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

with (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

m =
`(4-1)/(3+6)` =
`(3)/(9)` =
`(1)/(3)`

The line crosses the y- axis at (0, 3) ⇒ c = 3

y =
`(1)/(3)` x + 3 ← linear equation