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Q: How do you know that two equations are equivalent by looking at their graph?

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So people looking at the chart or graph will know what it depicts.

If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".

When you are solving a system of linear equations, you are looking for the values for the unknown variables (usually named x and y) that make each equation in the system true. Instead of using algebraic substitution or elimination, you can use graphing to find the variables. If you graph each equation on the same graph, the point where the graphs cross is the answer, which should be given as an ordered pair in the form (x,y). If the graphs do not cross anywhere (for example, parallel lines) then there is no solution. If the graphs of two lines end up being the same line, then there are an infinite number of solutions. You must know how to graph a line in order to use this method.

since there'll always be a time when one or two don't work. also, it's easier to check work by using another strategy

well, if you know all the formulating equations it will make you better at regular equations and regular equations can be used in everyday life

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by looking at it

They will be on the horizontal x axis of the graph (look for the x-intercepts).

The mode has two or more bars on the graph with the same height.

So people looking at the chart or graph will know what it depicts.

Well I'm a design engineer and I use them all the time. If I know a few values that are true for say, power versus cost for an car engine, then I can make sensible estimates for the cost of more powerful car engine that hasn't been built yet. Equally I could use graph equations to get the answers for the power I could expect from a cheaper engine. That's obviously just one of millions of possible applications to graph equations. You use them in Engineering, Design, Accountancy, Business, IT, Marketing, Banking, in Medicine, and in daily life for anything if you know how - take an iPhone for example, it works out how much battery it has left using a graph equation. An engineer built that into it.

If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".

When you are solving a system of linear equations, you are looking for the values for the unknown variables (usually named x and y) that make each equation in the system true. Instead of using algebraic substitution or elimination, you can use graphing to find the variables. If you graph each equation on the same graph, the point where the graphs cross is the answer, which should be given as an ordered pair in the form (x,y). If the graphs do not cross anywhere (for example, parallel lines) then there is no solution. If the graphs of two lines end up being the same line, then there are an infinite number of solutions. You must know how to graph a line in order to use this method.

what do you mean? how do you know a graph has no automorphisms? what do you mean? how do you know a graph has no automorphisms?

since there'll always be a time when one or two don't work. also, it's easier to check work by using another strategy

well, if you know all the formulating equations it will make you better at regular equations and regular equations can be used in everyday life

If I can't see the graph then how will I know the answer?

You need to know what the graph points are.