This week in math 10 we learned different forms of equations based on slope. One equation was the slope y-intercept ( y = mx + b, where m is the slope of the line and b is the y-intercept), another equation was general form (Ax + By + C = 0 where this equation has no relation to y intercepts or slopes. Not the most useful equation), the last equation is the slope-point form y-y₁=m(x-x₁) where m is the slope and y1 and x1 are one coordinate that the line goes through. The easiest and most useful equation. These equations are all easy to change into each other.

Slope-Point Form to Slope Y-Intercept Form to General Form

If we are given coordinates (-4,2) and the slope -1/3

First we figure out which equation to use and I chose slope=point form because we are given the variables needed to complete the formula.

m(x-x1)=y-y1

-1/3(x+4)=y+2

Now we distribute

-1/3x – 4/3 = y+2

Thenwe just solve the most we can

-1/3x – 10/3 =y

Now we already have it in slope y-intercept

Then to general form we need to multiply everything by the denominator which is 3 for both of them

-x -2 = 3y

Now we need y to equal a 0 so we could subtract 3y from both sides but we want x to be positive so I am going to take -x and -2 and switch them to the other side of the equal sign

x+3y+2=0

That’s in general form

This week in Math 10 we started a new chapter called linear relations ( any change in an independent variable will always make a change that is in agreement to the dependent variable.)  which is pretty much what we just learned, but a relationship that is the same proportion so when it’s placed on the graph it creates a line.

To find the slope, you must do rise divided by run 

Step 1: Find the rise. The rise is how much the slopes goes up . It corresponds with the y value. Count the difference between the y values.                                                                     In my example, the y values were -3 and 8. The difference is 11 and since the rise is going up, that means its positive.

Step 2: Find the run. The run is how much the slope moves to the sides. It corresponds with the x values. Count the difference between them.                                                                    In my example, the x values are 3 and 5. The difference between them is 2. Since it moves to the right, it’s considered positive.

Step 3: Find the slope. Divide the rise by the run.                                                                   In my example, the rise was 11 and the run was 2 and those divided equals 5.5 which is the slope. Or you can leave it as a fraction.

In Math 10 this week we stated a new unit called Relation and Functions. Relations are when the the independent variable, x, has multiple connections to dependent variables, y. Functions are when each independent variable has a special connection to one dependent variable.

Often written as f(x), if f(x) = 3x + 5

f(9) = 3(9) + 5

f(9) = 32, where the x variable, 9, has the pair of 32 as the y variable                                      on a graph. This would be a point of the graph. Another way of putting                                      this in words is that 9 is the domain and 32 is the range.

Domain is the set of all the numbers for the independent variable in the relation or function.    Range is the set of all numbers for the dependent variable in the relation or function.            So if we were given the domain { -2, -1, 0, 1, 2 } and the function f(x) = 3x^2 -4 then we can find the range { 8, -4, -1} because all we have to do is replace x in the expression with each number of the domain individually and solve.

These have a connection to the last unit we learned with expressions because often there are inputs that are integers and the output are expressions we were introduced to before.