Transcript of Writing and Graphing Equations
Write and Graph System of Equations There are three types of answers. There are one solution answers. There are, also, no solution answers. Then, there are infinately many solutions answers. When there are one solution answers, there are two intersecting or perpendicular lines. Intersecting and perpendicular means two lines that meet at a defined point. This is when two lines are parallel. Parallel is when two lines will NEVER intersect. This is when the two lines are equaled to the same answer so they overlap, causing the illusion of one, single line. How do I know wheither the two lines are perpendicular or parallel? If the two lines are perpendicular, crossing at 90 degree angles then their slope will be opposite reciprocals . Take these problems for example... 2x+6y=(-3) and (-3x)+y=(-8) After putting these problems into slopoe-intercept form, their slopes will be (-1/3) and 3/1. (-1/3) is a reciprocals to 3/1, therefore, the two lines are perpendicular If the two lines are parallel, then their slopes will be the same. Take these problems for example... x+5y=2 and (-10y)-2x=0 After putting these problems into slope-intercept form, their slopes will be (-1/5) and (-1/5) (-1/5) and (-1/5) are equal, therefore they are parallel. Is it possible to have neither perpendicular at a 90 angle or parallel? Take these problems for example... x+2y=6 and 2y=x+4 After putting these in slope- intercept form, their slopes are (-1/2) and 1/2. Since these slopes are not equaled to eachother or are not reciprocals, therefore their graphs will not be perpendicular or parallel. What is slope-intercept form and what is slope? slope-intercept is an equation that will help you determine slope. y=mx+b Y-Intercept The place where the line crosses through the y axis. Slope The angle of a line,written as rise/run. Slope is how steep a line is and how far it's angled. To graph the equations, you must know that the slope is written as rise/run. Rise is the height of the slope. It tells you how far up or down you go to graph slope. Run is how far you go from the y axis. Its is the length of the slope What is the system of equations? System of equations is a format for finding the answer for an equation with two variables. How do I put an equation in slope-intercept form? How do I graph equations? You could also use another formula to find the slope. y-y2Full transcript
x-x2 If you dont have any equation, but you have cordonate grid points then you can use this formula If you had a problem that looks more like (2,3) and (5,2), then you could solve it by putting it in this format. o These lines are perpendicular, but not at a 90 degree angle. Try this problem... Let's say you have a problem with cordinate grip points like (6,2) and (5,1) First, you need to find X and Y, where each number stands in the formula. Then you put the cordinate points in the formula to find slope. Then reduce your fraction. Now, you have the slope so we need to graph it. Then, let's say you also have an equation like 9x-3y=6. First, you must put it in slope-intercept form. Here you see that the y-intercept is (-2) and the slope is 3/1. The two lines cross at this point. This is the cordinate point (-1,0). This problem is a one solution answer because they intersect at one defined point. The answer is (-1,0). Thankyou for listening to my prezi-tation.