formula for equation of line through (1,3) and (3,4) ?

[lil_cougar]

Please help I can get most of it except this one.

Find an equation of the line containing the given points (1,3) and (3,4) the equation of the line is y = 1/2x+5/2 . I have that but how did they get that answer?

 

[Loren]

I would use two formulas.

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)
\(\displaystyle y-y_1=m(x-x_1)\)

Or, of course, you can combine those into one formula...
\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

 

[tkhunny]

You should have various "forms" of a line.

y = mx+b might be called the Slope-Intercept Form
y-y1 = m(x-x1) might be called the Point-Slope Form (x1,y1) is a given point.
y-y2 = [(y1-y2)/(x1-x2)](x-x2) might be called the Two Point Form (x1,y1) and (x2,y2) are given points.
x/a + y/b = 1 might be called the Intercept Form (a,0) and (0,b) are the x- and y-axis intercepts.
ax + by +c = 0 might be called the Standard Form
xcos(a) + ysin(a) - p = 0 might be called the Normal Form 'a' is the angle of the normal and p is the distance from the origin along the normal.

You won't necessarily know all of these, but you should have the ones you need for a problem assigned and expected to be solved.

In this case, you have two points. Use the Two Point Form. Really, that's all there is to it.