In order to find the slope of a line when given two points, you must use the equation

, with  standing for slope. 

In the equation  is the  coordinate of the second point,  is the  coordinate of the first point,  is the  coordinate of the second point, and  is the  coordinate of the first point. Therefore,

, , , and .

Once you plug in all the numbers into the equation for slope, you get

which simplifies to 

, or .

Therefore, the slope is .

In order to find our slope, we'll need to use the slope formula, which is 

To find out what number goes where, know that whatever coordinate comes first is coordinate  and the one following that is coordinate . Also know that  comes before  in a coordinate.

In math terms, our coordinates should look like this: 

Following this guide, we know that  must be ,  must be ,  must be and  must be .

Now that we know what goes where, place the numbers into the formula and solve for m:

Subtracting a negative is the same as saying adding a positive number. If this confuses you, then try this rule of thumb:

Leave, change, opposite. 

This is how you determine if the equation will add or subtract if you have wonky equations such as subtracting a negative. You leave the symbol of the first number alone and you change the second symbol as well as the third.

Let's look at  for this.

 can be rewritten as . We leave the positive  alone, change the subtraction to adding, and then make opposite of the negative , which would be positive .

This changes our equation to , which can be rewritten to .

Now that we know how to subtract a negative, our equation should be , which can be simplified to  since  goes into  twice.

Our answer is 

In order to reach the answer, we must first employ the slop formula; . 

To figure out what number goes where, know that whatever coordinate is given first in the answer is our coordinate , and the one following that is our coordinate . Also remember that  comes before  in a coordinate.

In math terms our coordinates should be . Following this example, our  must be , our  must be , our  must be  and our  must be .

Now that we know what goes where, plug in the numbers to our slope formula and solve for m:

Because  is the same number, we get . 

Our answer is 

In order to find the slope, you'll need to use the slop formula, which is .

Our  is , our  is , our  is  and our  is .

If you're confused on why I labeled our numbers like this, know that whatever coordinate your given first is your coordinate  and your next coordinate is coordinate . 

In math terms, our coordinates look like this .

Now that we know what number goes where, it's just a matter of solving the equation for .

Now we could leave our answer like that, but our fraction can actually be reduced even further. See how both the  and the  are divisible by ? Because they share this , we can divide both the  and  in order to get the smallest fraction without changing what the fraction stands for.

If you're confused on why we can do this, pick up a calculator and find out what the decimal equivalent of  is, then with .

Did you get the same answer? That's because  and  are the same answer, but  is just a smaller version of . It's the same for if we multiplied with , , or . Give it a try when you have the chance!

Our final answer should be 

For this problem you are given two values, the coordinates of a point, and the slope. The missing value is the  intercept. You therefore need to plug in what you know to the slope-intercept equation -  - and solve for what you don't know.  is the  coordinate of your point,  is the slope,  is the  coordinate of your point, and  is the  intercept. So, you know , , and  and you need to solve for .

Once you plug in  for ,  for , and  for , you get , which simplifies to . After you subtract the  from both sides of the equation, you find out that . Therefore, your  intercept is .

Find the y-intercept of the following linear equation:

The y intercept is where a line crosses the y-axis. At this point, our x value must be 0.

To find our y intercept, we simply need to plug in 0 for x and solve for y.

So, our answer is:

Find the slope of the following linear equation:

We can find the slope by solving this equation for y.

First, add 48 to both sides

Next, divide both sides by 4

Now, our slope is simply the number attached to our x variable. In this case, it is 4

Find the x-intercept of the following linear equation:

The x-intercept is where a line crosses the x axis. At the x-intercept the y value must be equal to 0.

To find our x-intercept, we are going to plug in 0 for y and solve.

Next, divide by 16.

So as an ordered pair, our answer is:

Two parallel lines have the same slope, or are both vertical. Since the first line has slope , a line parallel to this line must have slope also.

Recall what the slope-intercept form of an equation looks like:

Start by writing the equation in point-slope form:

Simplify this equation and re-write it into slope-intercept form.

Since the value of  is , the y-intercept is located at .