To find the and intercept of a linear equation, find the points where and are equal to zero.

To do this, plug in zero for either variable and then solve for the other.

this yields:

First we must recognize that the equation is given in slope-intercept form, where is the slope of the line.

Two lines are perpendicular if and only if the product of their slopes is . In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope.

Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or .

To double check that that does indeed give a product of when multiplied by three simply compute the product:

First, reduce all values to a common base using properties of exponents.

Plugging back into the equation-

Using the formula

We can reduce our equation to

So,

First we must recognize that the equation is given in slope-intercept form, where is the slope of the line.

Two lines are perpendicular if and only if the product of their slopes is . In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope.

Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or .

To double check that that does indeed give a product of when multiplied by three simply compute the product:

If the square is inscribed inside the circle, in means the center of the circle is at (1,1). We need to also find the radius of the circle, which happens to be the length from the corner of the square to it's center.

Now use the equation of the circle with the center and .

We get

To find the slope of the tangent line, we must take the derivative.

By using the Power Rule we will be able to find the derivative:

Therefore derivative of is .

Now we plug in , giving us .

Simplifying an inequality like this is very simple. You merely need to treat it like an equation—just don't forget to keep the inequality sign.

First, subtract from both sides:

Then, divide by :

The graph has x-intercepts at x = 0 and x = 8. This indicates that 0 and 8 are roots of the function.

The function must take the form y = x(x - 8) in order for these roots to be true.

The parabola opens downward, indicating a negative leading coefficient. Expand the equation to get our answer.

y = -x(x - 8)

y = -x2 + 8x

y = 8x - x2

Therefore, the answer must be y = 8x - x2

1. Plug in wherever there is an in the above equation.

2. Perform the above operations.

First, reduce all values to a common base using properties of exponents.

Plugging back into the equation-

Using the formula

We can reduce our equation to

So,