Question

What is the equation of the line passing through the points (Two-fifths, StartFraction 19 Over 20 EndFraction) and (one-third, StartFraction 11 Over 12 EndFraction) in slope-intercept form

Answer 1

Answer: y = 1/2x + .75

Step-by-step explanation:

Slope-intercept form: y = mx + b

Step 1: Find the slope.

Solve for
`(y2-y1)/(x2-x1)`

`y2-y1 = (11)/(12) -(19)/(20)`

`x2-x1 = (1)/(3) -(2)/(5)`

To solve for the fractions you need a common denominator.

`y2-y1 = (11*20)/(12*20) -(19*12)/(20*12) = (220)/(240) -(228)/(240)=(-8)/(240) = (-1)/(30)`

`x2-x1 = (1*5)/(3*5) -(2*3)/(5*3) = (5)/(15) -(6)/(15)=(-1)/(15)`

To divide fractions you keep (the first equation), change (the division sign to multiplication), and flip (the second fraction).

`(y2-y1)/(x2-x1)=((-1)/(30) )/((-1)/(15) ) = (-1)/(30)*(15)/(-1) =(-15)/(-30)=(1)/(2)`

Step 2: Plug slope and a point into y=mx+b to solve for b.

`(11)/(12)` = (
`(1)/(2)`)*(
`(1)/(3)`)+b

`(11)/(12)` = (
`(1)/(6)`)+b

`(11)/(12)-(1)/(6)` = b

`(11*6)/(12*6)-(1*12)/(6*12)=(66)/(72) -(12)/(72) =(54)/(72)=.75`

b = .75

y =
`(1)/(2)+.75`