Question

Write the equation of the line that passes through (1, 3) and (4, 4) in standard form.

Answer 1

x-3y+8=0

Answer 2

you're finding the slope through the slope formula of (y2-y1)/(x2-x1) but the equation of a line can be found by using the point-slope formula, given by

y-y0 = m(x-x0)

you already know that m = 1/3 so you have part of the equation, the other part is just one of the points that it passes through, either one will do, but I'll do both just to show you that you end up with the same equation.

So for the first one (1, 3)

y - 4 = 1/3(x - 4) so now we simplify
y - 4 = (1/3)x - 4/3
y = (1/3)x - 4/3 + 4
y = (1/3)x + 2-2/3

so the equation of your line is the above result, your slope is 1/3 which you already know, and your y-intercept is 2 & 2/3 or 8/3. If we were to multiply everything by 3 removing the denominator, your equation would be

3y = x + 8

So now if we use the other point (1,3), the initial equation would look like this

y - 3 = 1/3(x - 1) so now simplifying
y - 3 = (1/3)x - 1/3
y = (1/3)x -1/3 + 3
y = (1/3)x + 2-2/3

which is what we had before with the other point, so now you can see that the point-slope formula will work for any point along the line, and give you the same equation, just as long as you know the slope.

Hope that helps.

Answer 3

find the slope, put in py. slope form, then multiply thru clearing fractions....move x an y terms to one side, constant on the other