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What else can I help you with?
How can an equation represent a shape?
Two-dimensional geometry. Each corner of the shape is given two reference co-ordinates (x,y). When you plot these points and join them together, you get the shape. It's like magic. So a square has four points (corners) and they might have the reference points: (0,0) (0,3) (3,3) (3,0) Can I edit the answer of this question to say this really doesn't answer the question? My question was more like how does: (x - h)2 + (y - k)2 = r2 represent a circle? Though more general to be like how can equations like that actually represent a shape?
Always use the vertex and at least points to graph each quadratic equation?
You should always use the vertex and at least two points to graph each quadratic equation. A good choice for two points are the intercepts of the quadratic equation.
Can points be used to represent abstract concepts?
Yes they can.
How do you find Slope intercept equation of given two points?
Use the equation; y=mx+b where m is the slope Use your 2 points as y and b (intercept)
What is the equation of the line that passes through the points (12 8) and (17 16)?
Points: (12, 8) and (17, 16) Slope: 8/5 Equation: 5y = 8x-32
Is the two points form equation the same as linear equation?
The equations are equivalent.
What are equations with the same solution?
Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.
What is the concept of graphing system of equations?
You take each equation individually and then, on a graph, show all the points whose coordinates satisfy the equation. The solution to the system of equations (if one exists) consists of the intersection of all the sets of points for each single equation.
What is the quadratic formula used for today?
The quadratic formula is used today to find the solutions to quadratic equations, which are equations of the form ax^2 + bx + c = 0. By using the quadratic formula, we can determine the values of x that satisfy the quadratic equation and represent the points where the graph of the equation intersects the x-axis.
How do you solve systems of equations by graphing?
-- Graph each equation individually. -- Examine the graph to find points where the individual graphs intersect. -- The points where the individual graphs intersect are the solutions of the system of equations.
What type of system equation produces the solution set infinite solution?
If the equations of the system are dependent equations, which represent the same line; therefore, every point on the line of a dependent equation represents a solution. Since there are an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 3x + 2y = 8 6x + 4y = 16
What information does the graph of a function provide with respect to the algebraic equation?
The coordinates of the points on the curve represent solutions of the equation.
What does the line represent when you graph a linear equation?
It is the locus of all points whose coordinates satisfy the equation of the line.
What is the equation of the line that passes through 1 5 and 4 11?
Plug both points into the equation of a line, y =m*x + b and then solve the system of equations for m and b to get equation of the line through the points.
How do you find the equation of a parabola in standard form given 3 points?
I suggest that the simplest way is as follows:Assume the equation is of the form y = ax2 + bx + c.Substitute the coordinates of the three points to obtain three equations in a, b and c.Solve these three equations to find the values of a, b and c.
What is a system of equations that has infinite solutions?
When the two equations actually represent the same line, the solution to the system will be all points on the line. For example take the line y=x+2, if we multiply both sides of the equation by 2 we do not change anything about the line. So the equation 2y=2x+4 is really the same equation. The solution to the system y=x+2 and 2y=2x+4 is all the points ( all the real numbers) on the line. We often write this {(x,y)|y=x+2}
Why is it impossible to find all of the solutions of an equation with two variablevariables?
It is impossible to find all solutions of an equation with two variables because such equations often represent a continuous set of solutions rather than discrete points. For example, a linear equation in two variables typically describes a straight line on a graph, which contains infinitely many points. Additionally, certain equations may have complex solutions or involve parameters that further complicate the solution set, making it impractical to list every possible solution.
