Question

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

Answer 1

We can use the point-slope from of a line to find this equation. The general equation is:

`y-y_(1)=m(x-x_(1)`

So then, if the subscripted letters are respective to the point (2, -1/2), and m is equal to the slope (3) then we can put together the equation:

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

Then we can simplify:

`y+(1)/(2) =3x-6`

`y=3x+5(1)/(2)` or
`y=3x+(11)/(2)`

Answer 2

Equation of line is:

`y=3x-(13)/(2)`

Explanation:

Let equation of line be y=mx+c

where m is the slope of line and c is the y-intercept

Line passes through (2, -1/2) and has a slope of 3

i.e. (x,y)=(2, -1/2) and m=3

i.e.

`-(1)/(2)=3* 2+c\\ \\c= -(1)/(2)-6\\ \\c= -(13)/(2)`

So, equation of line is:

`y=3x-(13)/(2)`