this week in math we learned about systems in linear equations. A system in a linear equation is where 2 lines meet. You can solve this by taking the 2 equations, x + 2 = y and 3x + 4y = 1. you need to get a variable by its self on one side of the equation like y in x + 2 = y. Now, you have to put the x + 2 into the other equation in place of the y so you would get 3x + 4(x + 2) = 1 and then expand it to get 3x + 4x + 8 = 1 and add the like terms but put the numbers without a variable to the other side of the equation to get 7x = -7 and now divide to get x = -1. To get the y you need to add the x into one of the equations (the first one is easier) to get -1 + 2 = y and solve to get y = 1.
this week in math we learned how to make 2 points ((7,5) and (6,1)) on a graph into a general equation. First, you need to find the slope of the 2 points, to do this you need to subtract the 2 x’s and 2 y’s from each other but make sure you subtract the second point by the first point. ( so 1-5 and 6-7 to get -4/-1, y goes on top) now you put the slope in front of the x and subtract the x by one of the x points ( -4/-1(x – 7)) and on the other side of the equals sign subtract y by the same point on the y-axis. ( -4/-1(x-7) = y – 5) and now the equation is in point-slope form. to turn it into general form you need to distribute the slope. ( -4x + 28 = y – 5) Move everything on one side of the equation to the other and switch the sing of it, now add the like terms and the equation is in general form.(-4x – y + 23 = 0)
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 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.