Question

Write the point slope form of the line that passes through (-1, 4) and has a slope of -2/3.

The answer is y= -2/3x+ 10/3, but I have no idea where that 10 came from.

Plugging everything in:
4= -2/3 (-1) +b
4= 2/3 +b
cancel out 2/3 with -2/3, and put -2/3 under 4.
So, 4 - 2/3 = {2/3-2/3} + b

And somehow 4-2/3 = 10/3. HOW? I get where the 3 comes from, but I can't say the same for 10.

Answer 1

y-4=-2/3(x+1)
y-4=-2/3x-2/3
y-4+4=-2/3x-2/3+4
y=-2/3x-2/3+12/3 12/3=4
y=-2/3x+10/3

Answer 2

the 10 comes from -2/3+12/3

Answer 3

I am completely lost. Where does the y-4 come from? And why are you adding it to the second half of the equation? I'm guessing to get y by itself? But I'm still not sure why Y wasn't by itself to begin with. Also, where did the 12/3 come from? I'm sorry, but this is really confusing me. I tried to "draw it out" to make sense of it visually, but it didn't work. If it's not too much trouble, would you be able to draw it out so I can see the exact steps you made? Sorry about this. :(

Answer 4

And somehow 4-2/3 = 10/3. HOW

Answer 5

\[4-\frac{2}{3}=\frac{12}{3}-\frac{2}{3}=\frac{10}{3}\]

Answer 6

\[y – y1 = m(x – x1)\]
This is the point-slope formula. Does that help at all?

Answer 7

@satellite73 - I still have no idea where the 12 is coming from. :/ Sorry.
@gypsy1274 - I'm about to play with the equation to see what I come up with. We never went over that in class. At all.

Answer 8

*formula

Answer 9

the twelve comes from the fact that \(4=\frac{4}{1}=\frac{4}{1}\times \frac{3}{3}=\frac{12}{3}\)
if you want to add or subtract, the denominators have to be the same

Answer 10

Using this formula, you just plug in the numbers and then solve the equation for y. The ordered pair in the question are the values you will use for \(x_1\) and (y_1\). The slope is m.

Answer 11

I think you were originally trying to plug the ordered pair in to the \(y=mx+b\) formula, but that only helps if the ordered pair you have is the y-intercept.

Answer 12

@satellite73 - Ok, so I think I get where you're coming from. I'm going to need to practice this, but it makes a lot more sense now. Thank you.

@gypsy1274 - It's what my teacher said to do. Like I said, he never mentioned the formula you brought up, and I have no idea why. =/ *Currently using it to see what I get*

Answer 13

Maybe the example given in class used the y-intercept. To be honest, it is good practice for the teacher not to give all of the necessary information. Give the students sufficient information to find everything they need. It is frustrating to the students, but in the long run, it will help students to learn how to learn independently which is a big plus in the job market.