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There are lots of equations that don't form a straight line when graphed; for example:
- The independent variable occurs in any power other than one, for example: y = x2 or y = x3.
- The independent variable occurs in the denominator, for example: y = 1/x.
- If the equation involves some function, in most cases you won't get a straight line, for example: y = sin(x), y = sqrt(x) (i.e., the square root of x), y = ln(x) (the natural logarithm), any other logarithm, etc.
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Do graphs represent equations?
Bar graphs and line graphs do not. Straight line, parabolic, and hyperbolic graphs are graphs of an equation.
How do you know if two equations are parrallel?
If the slopes of a straight line equation are the same but with different y intercepts then they are parallel.
How do you write an equation for a line that passes through point and is parallel to the given line?
Both straight line equations will have the same slope or gradient but the y intercepts wll be different
Which graph could be used to find the solution of the system of equations y equals 2x plus 6 and y equals x2 plus 4x plus 3?
One way would be to graph the two equations: the parabola y = x² + 4x + 3, and the straight line y = 2x + 6. The two points where the straight line intersects the parabola are the solutions. The 2 solution points are (1,8) and (-3,0)
Can a system of linear equation have more than one solutions?
No. A linear equation represents a straight line and the solution to a set of linear equations is where the lines intersect; two straight lines can only intersect at most at a single point - two straight lines may be parallel in which case they will not intersect and there will be no solution. With more than two linear equations, it may be that they do not all intersect at the same point, in which case there is no solution that satisfies all the equations together, but different solutions may exist for different subsets of the lines.
What equations are helpful in GCSE further maths?
Quadratic, simultaneous and straight line equations
What is function as equations in two variables?
Straight line equations have two variables in the form of x and y
Who discovered equations of a straight line?
The French mathematician Rene Descartes
Why is linear equations called linear equations?
Because its linear and the equation is a problem to solve
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
Do graphs represent equations?
Bar graphs and line graphs do not. Straight line, parabolic, and hyperbolic graphs are graphs of an equation.
Can graphs be written as a equation?
Yes as for example straight line equations can be plotted on the Cartesian plane
What is the name of an equation that shows hoe one variable is related to one or more variables?
You maybe thinking of straight line equations or simultaneous equations
How are linear equations similar or different from functions?
A linear equation is a specific type of function that represents a straight line on a graph. While all linear equations are functions, not all functions are linear equations. Functions can take many forms, including non-linear ones that do not result in a straight line on a graph. Linear equations, on the other hand, follow a specific form (y = mx + b) where the x variable has a coefficient and the equation represents a straight line.
What do you call the graphs that intersect at exactly one point which gives solution of the system?
They are straight line graphs that work out the solutions of 2 equations or simultaneous equations
How do you know if two equations are parrallel?
If the slopes of a straight line equation are the same but with different y intercepts then they are parallel.
Who is Rene Descartes and how did he change geometry?
He was a French mathematician and he conceived the idea of coordinated geometry and straight line equations
