Question

Find an equation of the line containing the given pair of points.

(1,5) and (3,6)

Answer 1

Find the slope: (5-6)/(1-3)

Now what?

Answer 2

Re-write y = mx + b as y = xm + b, then insert the points as follows:

5 = 1m + b
6 = 3m + b

Now, isolate b in both equations:

b = 5 - 1m
b = 6 - 3m

Now set b = b:

5 - 1m = 6 - 3m

Place like terms on the same side:

3m - 1m = 6 - 5

Combine like terms:

2m = 1

Isolate m:

m = 1/2

Now find b:

b = 5 - 1m
b = 5 - 1(1/2)
b = 5 - 1/2
b = 4 1/2

Therefore the equation of the line is:

y = 1/2 x + 4 1/2

or

y = 1/2x + 9/2

Answer 3

What?

Find the Slope: (5-6)/(1-3) = -1/-2 = 1/2
Write the Equation: (y-5) = (1/2)*(x-1)

Done.

Answer 4

Yes, but you didn't provide any kind of explanation whatsoever.

Answer 5

I could also have "done" the same thing you did, but no one would learn anything.

Answer 6

@MathFrustration Have you heard of the Two-Point Form or the Point-Slope Form? They should be in your arsenal.

Answer 7

Yes, I have heard of all those, however, my method only requires memorizing one formula:

y = mx + b

Answer 8

Thank you. That would be why I asked the OP.

If you have only an hour for a 30 question exam, you're in trouble!

Answer 9

Not true. You have to understand that I have included a full set of steps with explanation. A student who is familiar with y = mx + b with practice would be able to do this in little to no time at all.

Answer 10

Meanwhile, your student would be fumbling around trying to remember point-slope form, two -point form, slope form, etc.

Answer 11

So, if THE problem was wanting me to plot (-5,0) and (0,3) The slope would be 3/5, Which would make it y=3/5x+/- whatever b is.

Answer 12

If that was the case, then you would already have b, since it represents the y-intercept.

Answer 13

So you would have the slope and the y-intercept and would be able to write y = mx + b in no time flat

Answer 14

Knowing the intercepts, you can just write it down \[\frac{ x }{ -5 } + \frac{ y }{ 3 } = 1\] Please learn various ways to solve as many problem types as you can. With a little practice, you can begin to judge which was is easiest in which situation.

Answer 15

Plotting is definitely a great way to avoid having to memorize formulas

Answer 16

Using Hero's method, if it was (-5,0) and (0,3) I can find the slope is 3/5 then do the b=-5(3/5) and find the b= -3

Answer 17

And yet one's attempt to introduce as many methods as possible surely won't confuse the student beyond clarification.

Answer 18

So I got that right then.

Answer 19

Well, actually, if you use my method correctly, you would realize that (0,3) means
x = 0, y = 3. In other words, the y-intercept is 3 without doing any algebra.

Answer 20

Ok.