write and equation of a line that passes through points 2,3 and 2,7

Question

e.mccormick · Answer

Do you know how to find the slope and use the point slope formula after that to find the line?

anonymous · Answer

slope is y1-y2/x1-x2?

e.mccormick · Answer

Yes!  So use that to find the slope first.

anonymous · Answer

so the slope is 4?

e.mccormick · Answer

Nope.  This one is a bit of a trick.

anonymous · Answer

is it -4/0?

e.mccormick · Answer

Well, you get either 4/0 or -4/0, but the slope can only be one thing, not two.  Also, remember the rule about dividing by 0?

anonymous · Answer

so the slope is 0?

e.mccormick · Answer

Not quite.  0 is a good number here, but for technical reasons it is not correct.  Ever hear of things being undefined?

anonymous · Answer

oh yeah! now i remeber so because its undefined is there no equation?

e.mccormick · Answer

Well, there is an equation, but the x value stays the same.   When they are like this and the slope is like that, it means it is a vertical line.

e.mccormick · Answer

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e.mccormick · Answer

Now, if the slope becomes 0, then it is a horozontal line.

anonymous · Answer

Thank you! and if I have to do the same thing for the points 2,4 and 6,16 is the slope 3? and what do I do after that?

e.mccormick · Answer

They also call vertical an infinite slope.

e.mccormick · Answer

OK.  You know the slope is 3.  Now, seen the $y-y_1=m(x-x_1)$ form of a line?

e.mccormick · Answer

You just solved for m.

anonymous · Answer

Where does the 3 go in that equation?

e.mccormick · Answer

$$m=\frac{y_1-y_2}{x_1-x_2}$$m is slope.

e.mccormick · Answer

So this time around, $m=3$.

anonymous · Answer

ok so now do I use y=3x+b? and how do I know waht the other variables are?

e.mccormick · Answer

You need to use the point/slope form.

$y-y_1=m(x-x_1)$ y and x are the variables.  Then take a point, $(x_1,y_1)$ from either $(2,4)$ or $(6,16)$ and plug it in.

e.mccormick · Answer

Then you can distribute the slope and solve for y, which gets you the y intercept form.

anonymous · Answer

so I shoud be doing y-4=3(x-2) or 16-4=3(6-2)?

e.mccormick · Answer

The first.

anonymous · Answer

ok thank you!

e.mccormick · Answer

What do you get when done with that?

e.mccormick · Answer

$$y-y_1=m(x-x_1)\implies \
y=mx-mx_1+ y_1\implies \
y=mx+b$$
You get the same b no matter which point you use.  You just use only one point for the last part, not both.
$$y-16=3(x-6)\implies \
y-16=3x-18\implies \
y=3x-18+16\implies \
y=3x-2$$ or $$y-4=3(x-2)\implies \
y-4=3x-6\implies \
y=3x-6+4\implies \
y=3x-2$$
One last tip! Watch out for negative points on the grid.  You can't just ignore the negative sign.  It has to go in as part of the variable.  So if had been say a -2 it would have been $(x-(-2))$ so $(x+2)$.