Question

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



y=

Answer 1

y =
`(4)/(3)` x + 2

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 ) = (0, 2) and (x₂, y₂ ) = (6, 10) ← 2 points on the line

m =
`(10-2)/(6-0)` =
`(8)/(6)` =
`(4)/(3)`

The line crosses the y- axis at (0, 2 ) ⇒ c = 2

y =
`(4)/(3)` x + 2 ← equation of line