1. When a positive number is added, the line starts higher on the y axis.
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There are three ways to solve systems of two equations with two missing points. These ways are graphing, substitution, and elimination. Graphing the two equations using slope intercept form is by far the most simple method, especially when the equations can just be plugged into Desmos.com, as shown below. The second method, substitution, is a bit more difficult. In the two equations, 2m+n=6 and 5m+6n=1, one of the variables must be isolated. Subtracting 2m from each side of the first equation gets n by itself, leaving us with n=-2m+6. Now that we know what n is equal to, we can plug it into either equation. If we put it into the second equation, we get 5m+6(-2m+6)=1. Distributing 6 into the parenthesis leaves us with 5m-12m+36=1. Add like terms to get -7m+36=1. Subtract 36 from each side to get -7m=-35, so m=5. The third way to solve systems of equations is through elimination. First we want to get both of our lines to have the same variable, but one must be negative. We multiply the entire equation, in this case 2m+n=6 is being used, by -6. -6(2m+n=6)=-12m-6n=-36. We then add the equations together to get -7m=-35. Dividing -7 on each side gives you m=5, and we can receive our other point by plugging in the point as previously explained. My favorite method to solve systems of equations is substitution, because I spent the most time on it as an Algebra 1 student and just generally feel the most comfortable with it.
The equation y=mx+b is used to express the equations of lines. If given the points (1,2) and (3,4), first one must find the slope, which is expressed by the letter m. To find the slope, the equation is y2-y1 over x2-x1. To find this, we plug each number from the coordinates into the equation to get 4-2 over 3-1, or 2 over 2, which can be simplified to 1. Our equation is now y=1x+b. Pick one of the points and plug the coordinates into the equation. If we put (1,2) into the equation, it then looks like 2=(1)1+b. 1x1=1, so 2=1+b. Subtracting 1 from each side leaves us with b=1. y=1x+1. This can now be graphed.
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April 2015
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