What is the equation of a line that passes through the point (3,-4) and has a slope of 2?

The other methods given here all yield correct equations, however the name of the form used in some of these solutions is not.

The Slope-Intercept Form of a linear equation is:

y=mx+b,

where m is the slope of the line, and b is the y-intercept of the line.  x and y are the coordinates of any point on the line, (x,y).

You could plug the slope (2) in for m, and the x (3) and y (-4) values for the given point in for x and y, then solve for the missing value, b (our y-intercept).

-4 = 2(3)+b

-4 = 6+b        then subtract 6 on each side to get...

-10 = b           There fore we have a y-intercept of -10 and a given slope of 2 giving us an equation in Slope-Intercept form of

y=2x-10

The other form given in the other solutions, (y-y1)=m(x-x1) is actually called the Point-Slope form of a line and is derived from the slope-intercept form.  Using this form, we can plug in the same coordinates given for x1 (3) and y1 (-4), and the slope for m (2).

(y--4)=2(x-3)

y+4=2x-6           subtract 4 from each side...

y=2x-10...the same solution as above.