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