Category: Grade 10

This week but can I learn how to substitute systems. Substitution is where one equation is “substituted” into another equation. A system is a set of equations that you work with all at the same time.

For our first question we are going to use these 2 equations

Step #1:

First before we do the substitution we need to isolate the x in the first equation.

Step #2:

Now we re going to insert one equation into another.(substitute highlighted part in step one into x)

Now we have one coordinate.

Step #3:

Now we have y we need to find x so substitute the y we have into the equation.

Step #4:

put them into coordinates and that’s how you know where the two lines meet

This week in math 10 I learned the general form of an equation. Journal form is pretty much useless but it is easy to type in. First I will go over things that are necessary for an equation to be in general form.

The first number in general form must be positive. The next two numbers have to be integers and cannot be fractions. And the most important thing is everything is on one side of the equal sign.

now that I went over the key things that identify general form, let’s start with changing an  Point slope form  into general form.

Step #1:  The first step is to distribute to make it  more simplified.

Step #2: now we are going to want to subtract a six from each side so we can start moving things to the other side.

Step #3:  next we are going to move what’s left to the other side and because it is negative it will become positive.

For our next example we are going to be changing general form into a slope intercept form. It is going to be similar as what we did before but backwards.

Step #1: first  subtract the 2X to both sides of the equation which where it will become negative again.

Step #2: now we are going to add 15 on both sides of the equation.

Step #3: we need to isolate the variable so to do that we will divide both sides of the equation by 5.

Step #4: you are now left with a slope intercept form which now u can tell what the slope and y-intercept is. (Much more useful).

This week in math 10 we started our unit on slopes (rate of change). We learned how to tell if this was a positive, zero, negative or undefined by looking at the steepness of the slope. We also learned how to get a line when given a starting point (coordinate) and a slope (rise/run). Another thing I learned is how to find the slope with 2 coordinates.

First thing I will go over is how to identify if it is a positive, negative, undefined, or zero slope. What helps me remember the differences is the slope guy.

Positive: The slope is going up (green)

Negative: The slope is going down (red)

Undefined: The slope is vertical (Yellow)

Zero: The slope is horizontal (blue)

Now that you know how to tell what type of sleep it is just go onto how to find the line when given a coordinate and a slope.

Step one: find the starting point

For our example starting our starting point is (2,1)

Step 2:

Look at the given slope and graph the next points. -3/4 (rise/run)

Now that you know how to draw the line when given a starting point and the slope let’s try to find the slope when only given 2 coordinates.

Step 1: place the two coordinates into a T chart (9,10) and (15,12)

 

Step 2: find the difference between the first set of coordinates and the second set of coordinates.

Step 3: Place the numbers into the rise over run format. If possible simplify the answer.

This week and math 10 we learned about function notation. I learned how to solve it when there are different outputs and inputs in the equation. In my math post I am going to show 2 different examples to showcase my understanding of this topic. I will start by explain the parts of the equation.

Now you know the parts let’s start with an example using the equation above.

Example #1-

Step 1: Replace the x with the input number (11).

Step 2: Multiply the 2 by 11 and then add the output together with the 3.

Now that your understand how the concept works let’s do more difficult example.

Example #2:

Step #1- Replace x with the input (3x).

Step # 2- Distribute the 2 to the 3 and the x. Multiply the 2 with the 3x.

This week and next 10 I learned how to find the domain and range. Domain is the set of all input values that can be used for a relation (x-value). Range is a set of all output values that are used by a relation ( y-value).

To find domain you find when it ends from the right and the left (Green). To find range look for when top and bottom ends (Purple).

Let’s start with finding the domain. We begin by finding the smallest number that touches the right or left side. The smallest number in this case is -5. Now because the dots are closed we are going to use this symbol ≤.  After that we’re going to find the biggest number that touches the X axis. That number is 5 in this example. Let’s write out the equation. -5 ≤ x ≤ 5

now we are going to find the range. This time we are going to start by finding the smallest number that touches the top or bottom. The smallest number and the example is -5. Again the dots are closed so we are using ≤. Next find the biggest number. 1 is going to be our biggest number. Now put all the information together. -5 ≤ y ≤ 1

This week in math 10 we reviewed how to graph coordinates. I have graft coronets before and I remember a few things.

there are four parts to The graph. There is quadrant 1(+,+), quadrant 2 (-,+), quadrant 3 (-,-)and quadrant 4 (+,-)Right in the middle is the origin (0,0). Y axis is the vertical line, the X axis is the horizontal line.

Now you know the labels for each part of the coordinate let’s start with a question. We have the  coordinates (-3,3). First number is along the X axis, the second number is along the Y axis.

let’s do another example. (5,-2)

 

This week in math 10 I learned how to factor a trinomial. Factoring trinomial‘s is the opposite of multiplying them. You do the same thing as if you were multiplying but reverse. Before we remove the brackets now we put the brackets back.

Step 1- Find the product 

find factors of the last number.

Step 2- Find the sum 

from the list of factor pairs find a pair that add to the middle number (10)

Step 3- Now we know the numbers so put them into the equation and your done.

Check your answer-  Use Foil 

to check your answer use foil and once you’re done if it is back to the original equation your answer is correct.

FOIL review-

First

Outside

Inside

Last