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Suppose you have the points with coordinates (p, q) and (r, s)
then, provided p is different from r,
the slope of the line is (q - s)/(p - r) = m, say.
Then, if (x, y) is any point on the line,
(x - s)/(y - r) = m
That, after simplification, is the linear equation of the line.
This will be a lot simpler when you have numerical values for p, q, r and s rather than work algebraically throughout.
If p is not different from r, then the equation is x = p (or r), a vertical line.
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Is the two points form equation the same as linear equation?
The equations are equivalent.
When you graph linear equations by plotting points the points you plot should all be what?
... plotted accurately.
What is a system of equations that has a solution of all points on one line?
Linear system
What are the importance of linear equation?
They are the simplest form of relationship between two variables. Non-linear equations are often converted - by transforming variables - to linear equations.
There is a system of linear equations with exactly two solutions is it true or false?
False. There can either be zero, one, or infinite solutions to a system of two linear equations.
Is the two points form equation the same as linear equation?
The equations are equivalent.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
What are the linear systems?
A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
What are two or more linear equations using the same variables called?
A system of linear equations.
When you graph linear equations by plotting points the points you plot should all be what?
... plotted accurately.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
When are two equations independent?
Two equations are independent when one is not a linear combination of the other.
What is a system of equations that has a solution of all points on one line?
Linear system
What types of equations or inequalities describe points x y that lie on a circle?
Linear equations or inequalities describe points x y that lie on a circle.
Why are there usually two solutions to a quadratic equation?
In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.
What is true about a system of two linear equations that has no solution?
The two equations represent parallel lines.
Can there be more than one point of intersection between the graphs of two linear equations?
Normally no. But technically, it is possible if the two linear equations are identical.
