To find slope, we must find the change in y values divided by the change in x values, also called the rise/run. This is modeled below:
Slope = m = (y1 - y2)/(x1-x2) = (6-(-3))/(1 - (-6)) = (6+3)/(1+6) = 9/7
We can check that this answer is correct by consulting the graph. The graph shows a positive correlation (means that the slope should be positive), and if you count the graph unit squares, you get that the graph moves up 9 squares and over 7 squares between the two points shown, letting us know we got the right answer.
Hope this helps!
{x+2y+2z=0
{2x+y+z=3
{x-3y-z=1
{x+2y+2z=0
-
{4x+2y+2z=6
{-3x=-6 → x=2
{-3y-z=-1
+
{y+z=-1
{-2y=-2 → y=1
{2+2+2z=0 → 2z=-4 → z=-2
Final triple is
(2; 1; -2)
First convert the terms to fractional exponents
u = t^2/3 - 3t^3/2
differentiating
u' = 2/3 t^ (2/3 - 1) - 3* 3/2 t^(3/2 - 1)
= 2/3 t ^(-1/3) - 9/2 t ^(1/2)
= 2 / (3∛t) - 9 √ t / 2 in radical form
