this week in math we learned about the slope of a graph. in order to find the slope of a graph, you need to take the graph.
now, find 2 points on the graph where it goes on both an x and a y line like these ones: 

now you need to find how much you need to rise up from the first point to be on the same level as the second point and how much you need to go right to get to the second point like this: 

now you have to put the rise over the run so you would get 6/5 and that is your slope.

this week in math we learned how to find the distance and middle between 2 points of a graph. To find the middle between 2 points you first have to take the 2 coordinates (4,6) (8,5) add the x and last numbers of each pair together 4 + 8, 6 + 5, and divide the answer by 2. 12/2, 11/2 = (6, 5.5). to get the length between 2 points you can use a² + b² = c². take 2 points on a graph (-3,8) (6,-4) and find the distance between the x and y by subtracting them -3 – 6 = 9, 8 – -4 = 12 (9,12). now put them in the equation and square them 9² + 12² = c². 81 + 144 = 225. now find the square root of your answer. √255 = 15

this week in math we learned about how to determine if something is a function or just a relation. if its a function then an input will not have a different output every time you input the independent variable. Like this: See how the two 4 inputs have different outputs(7 and 14)

how you see  this on a graph is to see if anything on the x axis over laps each other. like this:  See on the 2 graphs that aren’t a function you can draw a vertical line and it would go through 2 lines. but if you drew a line on the one that is a function it would only go through 1 line.

this week in math we learned about domain and range in a graph. the domain of a graph is where the line or the points are confined to in the x axis, range is the same but with the y axis. you can find the domain by taking this graph

and seeing where the most left of the red line is. Take that point, draw a line up and down the graph like a wall that the line can’t pass and see what the x is for the wall(-3). you can use an equation like this: -3 ≤ x. that isn’t completed yet, the other side of x is missing. what you do to get the other side of x is take the most right point of the line and make a wall there too. take the number for x and you get -3 ≤ x ≤ 2. the graph should look like this

to get the range you do the same as the domain but with the y axis. take the most bottom point of the line and instead of seeing where the x is and drawing a vertical line, you need to see where the y is and draw a horizontal line like a roof and a floor. you would get -2 ≤ y. do the same to the top and you get -2 ≤ y ≤ 2.

this week in math we learned about x and y intercepts. an x intercept is when a point on a graph has a value of 0 for x, the intercept for y is when a point on a graph has a value of 0 for y.

but you can use a trick to find out what the other value is going to be on the graph. take y = 12 – 3x for example. in order to find out the value of x on the y intercept you make the y a 0 so you have 0 = 12 – 3x. now you have to balance the 2 sides by subtracting 12 to cancel the 12 on the side with the x but what you do to one side you have do to the other so the equation will look like -12 = -3x. now you can divide the x by -3 to get the x by it’s self but that means you also have to divide the -12 by -3. after you do that the equation is 4 = x the x will equal 4 when y equals 0.

this week in math we learned how to more easily factor trinomials.

take 3x² + 10x + 8 for example. what you want to do is multiply the leading coefficient (3) by the last number (8) and 3 x 8 = 24.

now you have to find out what equation gets the product of 24 but also has the sum of 10 (the number in the middle).

there is 1 x 24, 2 x 12, 3 x 8, 4 x 6. 4 + 6 = 10 so we know that’s what it is.

to get a binomial you have to arrange the parts of the equation in a box like this:

the first part of the equation (3x²) goes in the top left box, the last part (8) goes in the bottom right, the numbers you just figured out ( 6 and 4) in the other boxes with an x behind them.

now you have to see whats similar with the numbers by seeing what you can divide into them. like this

and now you have your answer (x + 2) (3x + 4).

it takes a bit to explain but it can work a lot faster in your head.

this week in math we learned how to get a binomial equation from the answer. what you have to do is take the answer x² + 18x + 56. You have to see what multiplies into the number on the end, so 56, 1 x 56, 2 x 28, 4 x 14, 7 x 8. now, you have to see which of the equations when you add them together, equal the middle number. when added, 4 + 14 equals 18 (remove the x behind the 18) so the equation for this would be (x + 4)(x + 14) or (x + 14)(x + 4) because the order doesn’t matter.

this week in math we learned how to multiply 2 binomials. All you have to do is multiply each term by each other the easiest way to multiply them is by using FOIL front, outside, inside, last. when you use it, it should look like this