In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in $\displaystyle y$ coordinates over the change in $\displaystyle x$ coordinates. In equation form it looks like 

$\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$, where $\displaystyle y_2, y_1$ are the $\displaystyle y$ coordinates, and $\displaystyle x_2, x_1$ are the $\displaystyle x$ coordinates.

For this example, we will let $\displaystyle y_2=-12, y_1=11, x_2=10, x_1=11$.

$\displaystyle \mbox{Slope}=\frac{-12-11}{10-(-6)}=\frac{-23}{16}=-\frac{23}{16}$

Below is a visual representation of what we just did. The orange arrow is $\displaystyle \vec{w}$.

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in $\displaystyle y$ coordinates over the change in $\displaystyle x$ coordinates. In equation form it looks like 

$\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$, where $\displaystyle y_2, y_1$ are the $\displaystyle y$ coordinates, and $\displaystyle x_2, x_1$ are the $\displaystyle x$ coordinates.

For this example, we will let $\displaystyle y_2=1, y_1=-5, x_2=11, x_1=-11$.

$\displaystyle \mbox{Slope}=\frac{1-(-5)}{11-(-11)}=\frac{1+5}{11+11}=\frac{6}{22}=\frac{3}{11}$

Below is a visual representation of what we just did. The orange arrow is $\displaystyle \vec{w}$.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=5 \\ \mbox{(x in initial point)}=2 \\ \mbox{(y in terminal point)}=10\\ \mbox{(y in initial point)}= 3$

$\displaystyle x=5-2=3$

$\displaystyle y=10-3=7$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < 3,7>$

Below is a visual representation of what we just did.

The blue line is our original vector, and the red line is the same vector, but begins at the origin rather than at the initial point. 

n order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=5 \\ \mbox{(x in initial point)}=-2 \\ \mbox{(y in terminal point)}=-10\\ \mbox{(y in initial point)}= 3$

$\displaystyle x=5-(-2)=7$

$\displaystyle y=-10-3=-13$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < 7,-13>$

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=1 \\ \mbox{(x in initial point)}=-6 \\ \mbox{(y in terminal point)}=1\\ \mbox{(y in initial point)}= -9$

$\displaystyle x=1-(-6)=1+6=7$

$\displaystyle y=1-(-9)=1+9=10$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < 7,10>$

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=-9 \\ \mbox{(x in initial point)}=2 \\ \mbox{(y in terminal point)}=1\\ \mbox{(y in initial point)}= -10$

$\displaystyle x=-9-5=-14$

$\displaystyle y=1-(-10)=1+10=11$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < -14,11>$

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=3 \\ \mbox{(x in initial point)}=6 \\ \mbox{(y in terminal point)}=-8\\ \mbox{(y in initial point)}= -13$

$\displaystyle x=3-6=-3$

$\displaystyle y=-8-(-13)=-8+13=5$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < -3,5>$

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=-1 \\ \mbox{(x in initial point)}=-4 \\ \mbox{(y in terminal point)}=-5\\ \mbox{(y in initial point)}= -9$

$\displaystyle x=-1-(-4)=-1+4=3$

$\displaystyle y=-5-(-9)=-5+9=4$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < 3,4>$

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=-3 \\ \mbox{(x in initial point)}=-4 \\ \mbox{(y in terminal point)}=10\\ \mbox{(y in initial point)}=12$

$\displaystyle x=-3-(-4)=-3+4=1$

$\displaystyle y=10-12=-2$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < 1,-2>$

Below is a visual representation of what we just did.

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are. 

$\displaystyle x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$\displaystyle y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\displaystyle \\ \mbox{(x in terminal point)}=1 \\ \mbox{(x in initial point)}=-7 \\ \mbox{(y in terminal point)}=9\\ \mbox{(y in initial point)}= 5$

$\displaystyle x=1-(-7)=1+7=8$

$\displaystyle y=9-5=4$

To write this in component form, we need to put our $\displaystyle x$, and $\displaystyle y$ into $\displaystyle < >$.

So the final answer is $\displaystyle < 8,4>$

Below is a visual representation of what we just did.