Question

Which equation represents a line that passes through (4,1/3)and has a slope of 3/4

Answer 1

y =
`(3)/(4)` x +
`(-8)/(3)` or 12y = 9x -32 or y - 1/3 =3/4(x-4)

Explanation:

The equation of a line in the slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

The other form is the point-slope form where the point (x₁, y₁) and a slope m are given, and you have to plug it into formula:

y – y₁ = m(x – x₁)

Here:

y - 1/3 =3/4(x-4)multiply both sides by 12 to loose fraction

12y -4 = 9(x-4) distribute

12y -4 = 9x -36 add 4 on both sides

12y = 9x -32 divide by 12

y =
`(9)/(12)` x +
`(-32)/(12)` simplify factions

y =
`(3)/(4)` x +
`(-8)/(3)`