An ordered is always written in the following format:

$\displaystyle a= (x, y)$

where x is the position on the x-axis, and y is the position on the y-axis.

If we look at point a, we find where it falls on the x-axis.  We can see that it's position on the x-axis is 1.  Then, we see where it falls on the y-axis. It's position on the y-axis is 4.  So, we can write the ordered pair for point a as

$\displaystyle a =(1, 4)$

We will do the same for b.  The position of point b on the x-axis is -5.  The position of point b on the y-axis is 2.  So, we can write the ordered pair for point b as

$\displaystyle b= (-5, 2)$

And finally for c.  The position of point c on the x-axis is zero.  The position of point c on the y-axis is -5.  So, we can write the ordered pair of point c as

$\displaystyle c= (0, -5)$

The following coordinate plane displays the different quandrants.

You can also see there is a point that has been graphed.  

That point is (-3, 4).  

Therefore, (-3, 4) can be found in the second quandrant of a coordinate plane.

The midpoint formula is

$\displaystyle (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

where $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ are the points given.  So, using the points

(-5, 6) and (1, 2) we can substitute into the midpoint formula and get

$\displaystyle (\frac{-5 + 1}{2}, \frac{6 + 2}{2})$

$\displaystyle (\frac{-4}{2}, \frac{8}{2})$

$\displaystyle (-2, 4)$

Therefore, the midpoint is (-2, 4).

When looking at a coordinate plane, draw the letter C in there making sure you connect all four quarters of the grid. The C should start in the top right corner, move to the top left, then bottom left, then finish in the bottom right corner.

The quadrants start with $\displaystyle 1$ and finish with $\displaystyle 4$.

Therefore the coordinates $\displaystyle (7, -5)$ means $\displaystyle 7$ to the right and $\displaystyle 5$ down which would place the coordinates in quadrant 4.

In the standard form equation of a line, , the slope is represented by the variable .

In this case the line $\displaystyle y=13x+17$ has a slope of $\displaystyle 13$.

Therefore the answer is $\displaystyle m=13$.

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which is

$\displaystyle m=\frac{Y-y}{X-x}$

We must then properly assign the points to the equation as $\displaystyle (X,Y)$ and $\displaystyle (x,y)$.

In this case we will make $\displaystyle (9,-7)$ our  and $\displaystyle (8,12)$ our .

Plugging the points into the equation yields 

$\displaystyle m=\frac{-7-12}{9-8}$

Perform the math to arrive at 

$\displaystyle m=\frac{-19}{1}$

The answer is $\displaystyle m=-19$.

In the standard form of a line $\displaystyle y=mx+b$ the slope is represented by the variable $\displaystyle m$.

In this case the line $\displaystyle y=15x+13$ has a slope of $\displaystyle 15$.

The answer is $\displaystyle 15$.

The equation of the line is written in slope-intercept form, $\displaystyle y=mx+b$, where $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept. In this example, the y-intercept is a negative number.

$\displaystyle y=4x-7$

$\displaystyle m=4$

$\displaystyle b=-7$

The y-intercept is the point at which the line intersects the y-axis.

It does this at .

We plug  in for  in our equation, $\displaystyle y=16x+91$, to give us $\displaystyle y=16(0)+91$.

Anything multiplied by  is , so $\displaystyle y=91$.

Our coordinates for the y-intercept are $\displaystyle (0,91)$.

In the slope-intercept form of a line, , the slope is represented by the variable .

In this case the line

has a slope of .

The answer is $\displaystyle m=15$.