0
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.
What else can I help you with?
Is the two points form equation the same as linear equation?
The equations are equivalent.
How do you differentiate linear inequalities in two variables from linear equations in two variables?
Linear inequalities in two variables involve expressions that use inequality symbols (such as <, >, ≤, or ≥), while linear equations in two variables use an equality sign (=). The solution to a linear equation represents a specific line on a graph, while the solution to a linear inequality represents a region of the graph, typically shaded to show all the points satisfying the inequality. Moreover, linear inequalities allow for a range of values, whereas linear equations specify exact values for the variables.
When you graph linear equations by plotting points the points you plot should all be what?
... plotted accurately.
What is the difference between the solution of a system of linear inequalities and the solution of a system of linear equations?
The solution of a system of linear equations consists of specific points where the equations intersect, typically yielding a unique point, infinitely many points, or no solution at all. In contrast, the solution of a system of linear inequalities represents a region in space, encompassing all points that satisfy the inequalities, often forming a polygonal shape in two dimensions. While equations define boundaries, inequalities define areas that can include multiple solutions. Thus, the nature of their solutions differs fundamentally: precise points versus expansive regions.
Can a system of two linear equations have exactly two solutions explain?
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
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.
How do you differentiate linear inequalities in two variables from linear equations in two variables?
Linear inequalities in two variables involve expressions that use inequality symbols (such as <, >, ≤, or ≥), while linear equations in two variables use an equality sign (=). The solution to a linear equation represents a specific line on a graph, while the solution to a linear inequality represents a region of the graph, typically shaded to show all the points satisfying the inequality. Moreover, linear inequalities allow for a range of values, whereas linear equations specify exact values for the variables.
When you graph linear equations by plotting points the points you plot should all be what?
... plotted accurately.
When are two equations independent?
Two equations are independent when one is not a linear combination of the other.
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.
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.
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.
