Question

PLEASE HELP!!!!
what would be the equation of a line (in standard form) to get from point A (3,4) to point B (5,1) ?
please include the work/or steps with the final equation.

Answer 1

Fern: I think you'd benefit more in the long run by learning how to solve these problems yourself. You're given two points, and as part of the process of writing the equation of the line connecting those two points, you'll need to calculate the slope of the line.
Do you know the formula for the slope to use when you know two points on the line?

Answer 2

@mathmale im almost certain given the 2 points, it would be m= y2 - y1 over x2 - x1, no?

Answer 3

Yes, that's 100% correct. Please try calculating the slope.

Answer 4

@mathmale 1/2 or .5? is that correct? and from there what?

Answer 5

Fern: Have you some way of showing me how you arrived at that result? Could you draw it, or use the equation editor (below)?

Answer 6

\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }=\frac{ ( )-( ) }{ ( )-( ) }?\]

Answer 7

Fill in the ( ) with the appropriate x and y values and calculate the slope.

Answer 8

@mathmale what i have so far:
5 – 4 = 1
5 – 3 = 2
m= ½
y= ½x + b

Answer 9

Nice work! You could now choose one of the two points and substitute its coordinates into your y=(1/2)x+b equation. This will enable you to find the value of b.
You could also have chosen to work with the point-slope formula, which I prefer, but go ahead and do the problem with y=(1/2)x+b.

Answer 10

@mathmale i got a final equation of y=1/2x+5 with b having the value of 5/2. is this correct? id really appreciate it if you can help me complete the same problem in point slope form.

Answer 11

Rather than comment on your first result, let's jump into finding the equation of the line using the point-slope formula y-y0 = m (x-x0). Simply substitute the value of the slope that you already have, and choose one or the other points, and substitute the coordinates of that point into the point-slope form equation, simplify, and you'll be done.

Answer 12

@mathmale before i continue, y - 4 = ½ - 3 <---- that is the correct set up?

Answer 13

@mathmale do i just leave it at that since it is simply asking for the equation?

Answer 14

y - 4 = ½ - 3 is almost correct. But it has no x. Remember, y-y0=m(x-x0).

Try this again.

You can check your results by substituting tghe coordinates of either of the given points into this point-slope formula (which you can leave as is). If the equation is true, the formula is correct. Otherwise, check again.

Great working with you. Unfort., I must get off the computer pretty quickly.

Hope to have the pleasure of working with you again!