Question

Which equation represents a line that passes through (2,-1/2) and has a slope of 3 ?

A.Y-2=3(x+1/2)
B. Y-3=2(x+1/2)
C. Y+1/2=3(x-2)
D. Y+1/2=2(x-3)

Answer 1

C.
`y + (1)/(2) = 3(x - 2)`

Explanation:

Given

`Point: (2,(-1)/(2))`

`Slope: 3`

Required

Equation of line

Let m represents the slope of the line;

m is calculated as thus

`m = (y - y_1)/(x - x_1)`

`where (x_1,y_1) = (2,(-1)/(2))`

`So; x_1 = 2; y_1 = (-1)/(2)`

`m = 3`

By substituting the right values in the formula above;

`m = (y - y_1)/(x - x_1)` becomes

`3 = (y - (-1)/(2))/(x - 2)`

Multiply both sides by
`(x - 2)`

`3 *(x - 2) = (y - (-1)/(2))/(x - 2) *(x - 2)`

`3 *(x - 2) = (y - (-1)/(2))`

`3 *(x - 2) = (y + (1)/(2))`

`3(x - 2) = (y + (1)/(2))`

`3(x - 2) = y + (1)/(2)`

Reorder

`y + (1)/(2) = 3(x - 2)`

Hence, the equation that represents the line is
`y + (1)/(2) = 3(x - 2)`