Question

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

Answer 1

Answer:

Equation of line is:

$y=3x-\dfrac{13}{2}$

Step-by-step 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.

$-\dfrac{1}{2}=3\times 2+c\\ \\c= -\dfrac{1}{2}-6\\ \\c= -\dfrac{13}{2}$

So, equation of line is:

$y=3x-\dfrac{13}{2}$

Answer 2

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:

$y-(-\frac{1}{2} )=3(x-2)$

Then we can simplify:

$y+\frac{1}{2} =3x-6$

$y=3x+5\frac{1}{2}$ or $y=3x+\frac{11}{2}$