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

$\displaystyle m = (y_{2} - y_{1})/(x_{2}-x_{1})$, with $\displaystyle m$ standing for slope. 

In the equation $\displaystyle y_{2}$ is the $\displaystyle y$ coordinate of the second point, $\displaystyle y_{1}$ is the $\displaystyle y$ coordinate of the first point, $\displaystyle x_{2}$ is the $\displaystyle x$ coordinate of the second point, and $\displaystyle x_{1}$ is the $\displaystyle x$ coordinate of the first point. Therefore,

$\displaystyle y_{2} = 7$, $\displaystyle y_{1} = 3$, $\displaystyle x_{2} = 3$, and $\displaystyle x_{1} = 1$.

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

$\displaystyle (7-3)/(4-2)$

which simplifies to 

$\displaystyle 4/2$, or $\displaystyle 2$.

Therefore, the slope is $\displaystyle 2$.

In order to find our slope, we'll need to use the slope formula, which is $\displaystyle \small m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

To find out what number goes where, know that whatever coordinate comes first is coordinate $\displaystyle \small 1$ and the one following that is coordinate $\displaystyle \small 2$. Also know that $\displaystyle \small x$ comes before $\displaystyle \small y$ in a coordinate.

In math terms, our coordinates should look like this: $\displaystyle \small (x_{1},y_{1}) (x_{2},y_{2})$

Following this guide, we know that $\displaystyle \small y_2$ must be $\displaystyle \small 5$, $\displaystyle \small x_2$ must be $\displaystyle \small 3$, $\displaystyle \small y_1$ must be $\displaystyle \small -5$and $\displaystyle \small x_1$ must be $\displaystyle \small -2$.

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

$\displaystyle \small m=\frac{5--5}{3--2}$

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 $\displaystyle \small 5--5$ for this.

$\displaystyle \small 5--5$ can be rewritten as $\displaystyle \small +5- -5$. We leave the positive $\displaystyle \small 5$ alone, change the subtraction to adding, and then make opposite of the negative $\displaystyle \small 5$, which would be positive $\displaystyle \small 5$.

This changes our equation to $\displaystyle \small +5 + +5$, which can be rewritten to $\displaystyle \small 5+5$.

Now that we know how to subtract a negative, our equation should be $\displaystyle \small m=\frac{10}{5}$, which can be simplified to $\displaystyle \small 2$ since $\displaystyle \small 5$ goes into $\displaystyle \small 10$ twice.

Our answer is $\displaystyle \small m=2$

In order to reach the answer, we must first employ the slop formula; $\displaystyle \small m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. 

To figure out what number goes where, know that whatever coordinate is given first in the answer is our coordinate $\displaystyle \small 1$, and the one following that is our coordinate $\displaystyle \small 2$. Also remember that $\displaystyle \small x$ comes before $\displaystyle \small y$ in a coordinate.

In math terms our coordinates should be $\displaystyle \small (x_{1},y_{1}) (x_{2},y_{2})$. Following this example, our $\displaystyle \small y_2$ must be $\displaystyle \small 10$, our $\displaystyle \small x_2$ must be $\displaystyle \small 8$, our $\displaystyle \small y_1$ must be $\displaystyle \small 4$ and our $\displaystyle \small x_1$ must be $\displaystyle \small 2$.

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

$\displaystyle \small m=\frac{10-4}{8-2}$

$\displaystyle \small m=\frac{6}{6}$

Because $\displaystyle \small \frac{6}{6}$ is the same number, we get $\displaystyle \small 1$. 

Our answer is $\displaystyle \small m=1$

In order to find the slope, you'll need to use the slop formula, which is $\displaystyle \small m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

Our $\displaystyle \small y_2$ is $\displaystyle \small 8$, our $\displaystyle \small y_1$ is $\displaystyle \small 2$, our $\displaystyle \small x_2$ is $\displaystyle \small 5$ and our $\displaystyle \small x_1$ is $\displaystyle \small 1$.

If you're confused on why I labeled our numbers like this, know that whatever coordinate your given first is your coordinate $\displaystyle \small 1$ and your next coordinate is coordinate $\displaystyle \small 2$. 

In math terms, our coordinates look like this $\displaystyle \small (x_{1},y_{1}) (x_{2},y_{2})$.

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

$\displaystyle \small m=\frac{8-2}{5-1}$

$\displaystyle \small m=\frac{6}{4}$

Now we could leave our answer like that, but our fraction can actually be reduced even further. See how both the $\displaystyle \small 6$ and the $\displaystyle \small 4$ are divisible by $\displaystyle \small 2$? Because they share this $\displaystyle \small 2$, we can divide both the $\displaystyle \small 6$ and $\displaystyle \small 4$ in order to get the smallest fraction without changing what the fraction stands for.

$\displaystyle \small \frac{\frac{6}{2}}{\frac{4}{2}}=\frac{3}{2}$

If you're confused on why we can do this, pick up a calculator and find out what the decimal equivalent of $\displaystyle \small \frac{6}{4}$ is, then with $\displaystyle \small \frac{3}{2}$.

Did you get the same answer? That's because $\displaystyle \small \frac{6}{4}$ and $\displaystyle \small \frac{3}{2}$ are the same answer, but $\displaystyle \small \frac{3}{2}$ is just a smaller version of $\displaystyle \small \frac{6}{4}$. It's the same for if we multiplied $\displaystyle \small \frac{6}{4}$with $\displaystyle \small 2$, $\displaystyle \small 3$, or $\displaystyle \small 4$. Give it a try when you have the chance!

Our final answer should be $\displaystyle \small m=\frac{3}{2}$

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

Once you plug in $\displaystyle 2$ for $\displaystyle y$, $\displaystyle 3$ for $\displaystyle m$, and $\displaystyle 1$ for $\displaystyle x$, you get $\displaystyle 2 = 3(1) + b$, which simplifies to $\displaystyle 2 = 3 + b$. After you subtract the $\displaystyle 3$ from both sides of the equation, you find out that $\displaystyle b = -1$. Therefore, your $\displaystyle y$ intercept is $\displaystyle -1$.

Find the y-intercept of the following linear equation:

$\displaystyle 4y-48=16x$

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.

$\displaystyle 4y-48=16(0)$

$\displaystyle 4y-48=0$

$\displaystyle 4y=48$

$\displaystyle y=12$

So, our answer is:

$\displaystyle (0,12)$

Find the slope of the following linear equation:

$\displaystyle 4y-48=16x$

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

First, add 48 to both sides

$\displaystyle 4y=16x+48$

Next, divide both sides by 4

$\displaystyle y=4x+12$

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

$\displaystyle m=4$

Find the x-intercept of the following linear equation:

$\displaystyle 4y-48=16x$

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.

$\displaystyle 4(0)-48=16x$

$\displaystyle -48=16x$

Next, divide by 16.

$\displaystyle \frac{-48}{16}=x$

$\displaystyle -3=x$

So as an ordered pair, our answer is:

$\displaystyle (-3,0)$

Two parallel lines have the same slope, or are both vertical. Since the first line has slope $\displaystyle -1.6$, a line parallel to this line must have slope $\displaystyle -1.6$ also.

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

$\displaystyle y=mx+b$

Start by writing the equation in point-slope form:

$\displaystyle y-7=\frac{1}{8}(x-16)$

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

$\displaystyle y-7=\frac{1}{8}x-2$

$\displaystyle y=\frac{1}{8}x+5$

Since the value of $\displaystyle b$ is $\displaystyle 5$, the y-intercept is located at $\displaystyle (0, 5)$.