Hello, isuckatcalc!

If you copied the problem correctly, your answer is correct.

i am given a picture of a triangle with vertices: .$\displaystyle A(0,3),\;B(2,0),\;C(0,\text{-}6)$

i need to find the equations of these lines in order to know the bounds of my integrals.

My solution was to first find the slope.

So for the line from A(0,3) to B(2,0), that would be (0-3)/(2-0) = -3/2.

Then plug in one of those points to find C, and i get 3.

So the line equation is y = -(3/2)x +3.

i was marked off and told to use point-slope form.

And my teacher came up with the equation y = -x + 2 .??

What is point-slope and how did i do this wrong?

i don't understand why my equation is not correct. Code:

|A
(0,3)o
| *
| *
| * B
- - + - - - o - - -
| *(2,0)
| *
| *
| *
| *
| *
|*
(0,-6)o
|C

Your teacher's line has a slope of $\displaystyle -1$ and a $\displaystyle y$-intercept of $\displaystyle 2$.

. . Neither feature is on the graph. .The error seems to be his/hers.

The Point-Slope Formula is one I recommend to all my students.

. . However, I do NOT insist that they use it.

Given a point $\displaystyle P(x_1,y_1)$ and a slope $\displaystyle m$

. . the line through $\displaystyle P$ with slope $\displaystyle m$ has the equation:

. . . . . . . . $\displaystyle y - y_1 \;=\;m(x-x_1) $

If you're using the Slope-Intercept form, $\displaystyle y \:=\:mx + b$

. . and you are given the slope *and* the y-intercept, you're golden!

If you are *not* given the y-intecept, you must perform

. . some extra acrobatics to get the equation.

The Point-Slope formula eliminates those extra steps.

. . It works for *any* point, not just the y-intercept.