Thread: Precalculus - Slopes

Find the slope m of the line in the following figure.


Thanks for the help!

Let's use the form y=mx+c.
Since the line passes through (2,1) we know 1=2m+c
We also know that the y intercept is c and by substituting y=0 we can discover that the x intercept is -c/m. Using the formula for the area of a triangle, we get $\displaystyle \frac12 (c)(\frac{-c}{m})=4$. Then it is just a matter of solving the simultaneous equations.

I'm sorry. I don't quite understand how to solve . Could you explain more, please?

Originally Posted by juicysharpie

Find the slope m of the line in the following figure.


Thanks for the help!

let eqn. of line be

x/a+y/b=1-----------------------intercept formula

since it passes through....(2,1)

2/a+1/b=1 .................................................. ....(1)

areaof triangle=4=1/2*ab

ab=8.............................................. .................(2)

solve these eqn. to find the values of a,b

then find the slope m=b/a

hmmm...I didn't learn that intercept formula. Is there another way to approach this problem?

Let's use the form y=mx+c.
Since the line passes through (2,1) we know 1=2m+c
We also know that the y intercept is c and by substituting y=0 we can discover that the x intercept is -c/m. Using the formula for the area of a triangle, we get . Then it is just a matter of solving the simultaneous equations.

$\displaystyle \frac12 (c) (\frac{-c}{m}) = 4 $
$\displaystyle \implies \frac{-c^2}{m} = 8$
$\displaystyle \implies m = -\frac{c^2}{8}$
substitute into 2m+c = 1

$\displaystyle
2(-\frac{c^2}{8})+c = 1$

can you continue?

Yes, I can. Thank you sooo much!

Is the answer m = -1/2?

Is the answer m = -1/2?

Yes it is. Well done.