This week in math we started a new unit and learned about the different kinds of solutions.

Here is an example:

One solution is when we have one intercept (one point where the lines cross each other) which means the slopes are different and in this solution the y intercepts can be the same or different. When is comes to infinite solutions, the lines are identical, same slope and same y intercepts. Finally there is no solution. This is when the lines are parallel to each other so they never cross. This means they have the same slope but a different y intercept.

This week in math we worked on learning terms like elimination and substitution.

Here is an example of elimination.

Here is our 2 equations and we are asked to use the method of elimination to figure out our missing variables which in this case are a and b.

Our first step we want to do is figure out which variable we will eliminate first. In this case i just chose A to start with.

In order to use the method of elimination we have to cancel out one of our variables in both equations and in order to do that u have to have one negative and one positive which is why i multiply the A with negative 2. I cant just multiply the A though, you need to multiply everything in the equation.

In the picture above i multiplied everything by -2 like i said we do, then i cancelled out our “like” variables by adding them together and then all that’s left was to add the other variables and simply which in our case we divided our answer by 7 on both ends leaving us with b=2.

We aren’t done there though, we still need to figure out what our variable “A” is. In order to do this all we need to do is plug 2 in wherever we see b.

In the image above i plugged 2 in wherever i saw B and then simply solved which left us with an answer of A=3.

This week in math we are wrapping up our slope unit and getting ready for our unit test.

Here is an example of something we learned this unit.

When we see a question like this, we have 2 options to solve. We have the slope formula which i am going to use or you have the T chart way.

I showed what the slope formula is and then i took our numbers in our brackets and plugged them into our equation.

The last step is to simply finish solving our equation. Since we have 2 negatives on our top half of our equation we add the 2 numbers together. Our final answer for trying to find our slope is 13 over 1 which is just 13.

This week in math we focused in on slopes.

Here is an image of all the different slopes that we learned about.

We learned how to graph different slopes that we are given and we learned how to figure out the slope when given a set of numbers.

Here is an example:

When we are given and set a numbers and told to find the slope we can do one of two things to figure out the slope. My favourite way is to use a formula which is shown in the image below.

This formula can help us get the slope fast and efficiently but the only thing we have to be careful of is when we have an input number that is a negative. Thankfully in this specific question all of our numbers are positives.

In this image all i did was use the formula to solve. I labeled our input numbers so u can visually see where i got my X and Y numbers from. I plugged them in accordingly and our final step is just to simplify (if possible which it’s not in some questions) which left our answer to be 15/4.

This week in math we mostly looked at the differences between functions and relations.

When you know what your looking for it can be easing to tell the difference between the 2.

This is a common visual we will see throughout this unit. We may be asked to figure out if the question is a function or relation by looking at something like this. We know if it’s a function or relation by being attentive to our X column which is on the left.

The first set of columns we see is going to be a relation. We can tell because if we look in our X column we notice that we have a set of 2’s and whenever we see a multiple of a number we know it’s not a function. On the other hand our second set of columns is a function because we don’t have a set of numbers in our X column.

This week in math we worked on linear relations. We worked on finding coordinates and learning how to read a graph.

Here is an example question we worked on this week.

For this question, as you can see, we are asked to find both the X and Y intercept.

In order to find the X intercept we need to get rid of our Y intercept which is why it is crossed off. But we still have to isolate our variable ( X ) so we have to take away the 7 on the end. Whatever we do to one side of our equation we have to do to the other which is why our final answer for X is going to be a fraction.

For our Y intercept we just do the opposite which is to get ride of X. We are left with an easier answer of 7 so we don’t need to do any subtracting.

Our final step is to put out answered in coordinate form.

Here is our final answer for this question.