Question

Use the slope intercept form of the equation to evaluate the equation at x=3 and x=11.
The equation:
y=2 x (5-3x11)-6+9x11

Answer 1

To evaluate the given equation at \( x = 3 \) and \( x = 11 \), let's first simplify the expression.

The equation you've provided is:

\[
y = 2x(5 - 3x11) - 6 + 9x11
\]

Looking closely, it seems like there might be a mix-up with the multiplication of \( 3 \) and \( 11 \). If we treat \( 3 \) and \( 11 \) as separate variables or constants, the expression can be clarified.

Let's rewrite the equation with proper multiplication:

\[
y = 2x(5 - 33x) - 6 + 99x
\]

Where \( 33 = 3 \times 11 \) and \( 99 = 9 \times 11 \).

Now we can rewrite the equation as follows:

\[
y = 2x(5 - 33x) - 6 + 99x
\]

Expanding this:

1. First, distribute \( 2x \):
\[
y = 10x - 66x^2 - 6 + 99x
\]

2. Combine like terms:
\[
y = (-66x^2) + (10x + 99x - 6) = -66x^2 + 109x - 6
\]

Now let's evaluate \( y \) at \( x = 3 \) and \( x = 11 \).

### For \( x = 3 \):

\[
y = -66(3)^2 + 109(3) - 6
\]

Calculate:

\[
y = -66(9) + 327 - 6
\]

\[
y = -594 + 327 - 6
\]

\[
y = -594 + 321
\]

\[
y = -273
\]

### For \( x = 11 \):

\[
y = -66(11)^2 + 109(11) - 6
\]

Calculate:
\[
y = -66(121) + 1199 - 6
\]

\[
y = -7986 + 1199 - 6
\]

\[
y = -7986 + 1193
\]

\[
y = -6793
\]

### Summary of Results
- At \( x = 3 \), \( y = -273 \)
- At \( x = 11 \), \( y = -6793 \)