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The slope is the rise over the run, or the change in y over the change in x. It describes how steep or shallow the slant of a line is on a coordinate plane.
A linear equation is the equation of a line that increases or decreases at a constant rate. A linear equation produces a graph that is a straight line.
Let x represent the distance driven, and let y represent the amount of gas in Jenna’s tank. Then the slope of the equation is –1gal/100mi and the y-intercept is 15. This means the equation is y = [ggfrac]1/100[/ggfrac]x + 15.
The substitution method is a method for solving a system of equations. In this method, one equation is set equal to a single variable and then substituted into the other equation.
The graphing method is a method for estimating the solution to a system of equations. In this method, two linear equations are graphed on the same coordinate plane. The point where the two lines intersect is the solution to the system.
No, I get the same answer no matter which variable I rearrange for, or which equation I rearrange first. There may be one variable that is easier to solve for first, in which case I may choose to solve that one first, but I don’t need to.
Yes; it is possible that a point is on one line and not the other. The solution to a system needs to be on both lines, so I need to check both equations.
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