Question

Find an equation for the linear function, H(x), shown in the graph below

Answer 1

y =
`(1)/(5)` x - 1

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) )`

let (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (5, 0) ← 2 points on the line

substitute these values into the formula for m

m =
`(0-(-1))/(5-0)` =
`(0+1)/(5)` =
`(1)/(5)`

the line crosses the y- axisat (0, - 1 ) so c = - 1

y =
`(1)/(5)` x - 1 ← equation of line