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How do you model your equation on a number line to show your answer?
You model your equation on a number line to using a bar model.
What is the point at which the lines intersect in a system of linear equations?
The coordinates of the point of intersection represents the solution to the linear equations.
Why do some systems of equations have one solution?
If it is a linear system, then it could have either 1 solution, no solutions, or infinite solutions. To understand this, think of two lines (consider a plane which is just 2 dimensional - this represents 2 variables and 2 equations, but the idea can be extended to more dimensions).If the 2 lines intersect at a point, then that point represents a solution. If the lines are parallel, then they never intersect, and there is no solution. If the equations are such that they are just different ways of describing the same line, then they intersect at every point, so there are infinite solutions. If you have more than 2 lines then maybe some of them will intersect, but this is not a solution for the whole system. If all lines intersect at a single point, then that is the single solution for the whole system.If you have equations that describe something other than a straight line, then it's possible that they may intersect in more than one point.
Does every line have a slope intercept equation?
No. Vertical lines and horizontal lines have undefined and 0 slopes. Undefined could be any number, so the answer is No. Good luck with your Apex :)
What points are on the line given by the equation y equals 5x?
Any point on the line is a solution to the equation, and any solution to the equation is a point on the line. Ie any point where the y coordinate is 5 times the x coordinate will be on the line; for example the points (0, 0), (1, 5), (2, 10), (-1, -5), (-2, -10) all lines on the line y = 5x.
