Question

Determine the standard form of the equation of the line that passes through (6,0) and (2,-7).

Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9)

Determine the standard form of the equation of the line that passes through (-7,8) and (0,2)

Determine the standard form of the equation of the line that passes through (0,5) and (4,0)

Answer 1

With 2 points, you can use the slope formula to find the slope.

Then use the point-slope form, with the slope you found and either point, to cook up the equation for the line:

\[\Large y-y_{1}=m(x-x_{1})\]

Just plug in your slope and one point, then rearrange the terms for standard form:
Ax + By = C where A>0 and and A, B and C have no common factors.

Answer 2

I don't know how to do that.

Answer 3

Which part? Given the two points, do you know how to find slope?

Answer 4

\[\Large \text{slope}= m=\frac{ y_2-y_1 }{ x_2-x_1 }\]

Answer 5

Yes, like for the last one it is -5/4

Answer 6

OK, good - that's right. so you have the slope, and you have 2 points. You want the equation for the line, and you want it in a particular form (standard form). don't worry too much about the "standard form" part for now. We can always get to standard form - let's just get an equation for the line.

Answer 7

Would you know how to get y=mx+b, slope intercept form?

Answer 8

Here is a hint that WONT work for all of these, but DOES work for the last one - one of your points has an x=0. What does that mean about the y-coordinate of that point?

Answer 9

I do not know how to get b. And I am not sure.

Answer 10

y - y1 = m(x - x1)

Answer 11

find the slope.
Then use either of the points (x1,y1) and sub them into the point slope formula.
y - y1 = m(x - x1)
solve for y.
then put it into standard form

Answer 12

Well, every point on the line has to satisfy (make true) the equation of the line. And you know slope, and you know points. So, for example, to find b, one method is just to put in your slope of m, and either point, to the form y=mx+b, and solve it for b. Let's try it with your 4th problem, since you already know the slope there.

You have m=-5/4
I'll use the point (4,0) and plug it all into: y=mx+b

so I get:

0=(-5/4)*4+b
0=-5+b
5=b

So b=5, that is, 5 is my y-intercept (the y coordinate of the point where the line crosses the y-axis).

Now, the "hint" I offered above is that one of the points has x=0. The point of that is that, the y-intercept is ALWAYS the y-coordinate of the point that has x=0, since every point on the y=axis has x=0. So if you have a point that has (0, ?) then the "?" is the y-intercept, for sure.

So now that we have b, we know the equation in SLOPE-INTERCEPT form is:

y=(-5/4)x+5

Are you with me so far? (Read this 2 or 3 times if you need to!)

Answer 13

Why do you multiply by 4?

Answer 14

Because I'm plugging in the point (4,0), to the line equation y=mx+b.

So x=4. It is multiplied with the slope, m.

Answer 15

x=4, y=0, m=-5/4.... looking for b.

y=mx + b -----> 0=(-5/4)*4+b

Do you see how I'm just put each thing into its place in the equation?

Answer 16

Yes, I do. Now how do you turn it into standard form?

Answer 17

OK, we have

y=(-5/4)x+5

And we want it to be of the form Ax + By = C. As I said above, A, B and C are all integers, and we like to have x positive.

The first think I'd like to do is get rid of that fraction, because I know that standard form doesnt have fractions (and it will be easier to work with the equation with out it, anyway).

I see that the fraction has a den'r of 4. Well, since I can multiply an equation by the same thing on both sides, how about I multiply both sides of this equation by the den'r, 4? Be careful to distribute on the right hand side.

4*y=[(-5/4)x+5]*4
4*y=4(-5/4)x+4*5

Now do you see the beauty of it?? The 4 multiplied by the fraction -5/4 will CANCEL with the 4 in the den'r:


4y=-5x+20

Tah-dah! No more fractions. With me so far?

Answer 18

oops, should say ^^ "and we like to have *A, the coefficient of x, positive." :)

Answer 19

Alright, I am with you. Is it 5x+4y=20?

Answer 20

Yes!! There you go - good job! :)

Answer 21

Thank you. (:

Answer 22

Now just follow the same procedure with the others:
1. find the slope
2. find the y-intercept (I said use point-slope form above, but if you understand the example, that method will work fine so just go with that)
3. Now you'll have the line equation in slope-intercept form. From there to standard form is just a couple of steps of algebra.

You're welcome. :)

Answer 23

I took a short quiz after your help and got an A! Thank you again. (: