Hello!

Ok so ideally we would like to see this in y=mx+b form. But it will take some algebreic skills to ninja our way through this.

I'll show my steps so you can follow,

3+4x = 2y - 9 (original equation)

Next we just add 9 to both sides,

12 + 4x = 2y, now we can divide both sides by 2,

y=2x+6 as our final equation. This is in y=mx+b form, thus the slope of our line is 2 because the 2 is sitting in the m space of the equation. If you still dont understand linear stuff, I'd google slope-intercept form

Hope this helped!

7 0

3 years ago

(a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve

Dafna1 [17]

Answer:

(a) y = 9/4x -1/4

(b) (-2, -2), (-2, 2)

Step-by-step explanation:

(a) The derivative can be found from ...

2y·y' = 3x² +6x

At (x, y) = (1, 2), this is ...

4y' = 9

y' = 9/4

so the equation of the tangent is ...

y = (9/4)(x -1) +2

y = (9/4)x -1/4

(b) At y' = 0, we have ...

0 = 3x² +6x = 3x(x +2)

This says y' = 0 at x=0 or x=-2. (x = 0 is an extraneous solution.)

At x = -2, we have ...

y² = (-2)³ +3(-2)² = -8+12 = 4

y = ±2

So, the horizontal tangent points are (x, y) = (-2, ±2).

5 0

3 years ago