+9468 the slope between two points \(=\,\frac{\text{difference in y values}}{\text{difference in x values}}\)
the slope between (2, 4) and (6, 3) \(=\,\frac{3-4}{6-2}\)
the slope between (2, 4) and (6, 3) \(=\,-\frac{1}{4}\)
And we know that the slope between (6, 3) and (-5, c) also equals -\(\frac14\) . So we know
\(-\frac14\,=\,\frac{c-3}{-5-6}\\~\\ -\frac14\,=\,\frac{c-3}{-11}\)
Multiply both sides of the equation by -11 .
\(\frac{11}4\,=\,c-3\)
Add 3 to both sides.
\(\frac{11}4+3\,=\,c \\~\\ c\,=\,\frac{23}{4}\,=\,5.75\)
Here is a graph to show that these points lie on the same line.
+9468 (x + 3)2 + (y - 3)2 = 6 Let's solve this for y .
(y - 3)2 = 6 - (x + 3)2
y - 3 = ±√[ 6 - (x + 3)2 ]
y = ±√[ 6 - (x + 3)2 ] + 3 So....using this value for y....
\(\frac{y}{x}\,=\,\frac{\pm\sqrt{6-(x+3)^2}+3}{x}\)
We can say
\(Y\,=\,\frac{\pm\sqrt{6-(x+3)^2}+3}{x}\) and we want to know the maximum Y value here.
We can get an approximation by looking at a graph. (about 5.828)
If you take the derivative and set it = 0, you will get x = √2 - 2
Then plug this in for x and we can find that the exact maximum value = 3 + 2√2
