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- Standard form: ax + by + c = 0 (a, b, c constants, x and y variables)
- Slope intercept form: y = mx + c (m, c constants, x and y variables)
- Two points form: given P = (a, b) and Q = (c, d)
(y - b)*(x - a) = (d - b)*(c - a ) (a, b, c, d constants, x and y variables) - Parametric equation x = a + r*cos(t), y = b + r*sin(t) (a, b, t constants, x and y variables)
- X = A + k*B (X, A and B vectors, k scalar, X and k variables).
The standard form, parametric equation and vector form have simple analogies for 3 or more dimensions.
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When lines overlap in a system of equations?
Then they are simultaneous equations.
What are the order pairs for 2x plus y equals 1 and 2x - y equals -5?
These are equations of two straight lines. Provided the equations are not of the same or parallel lines, there can be only one ordered pair. So the answer is - (not are) : (-1, 3).
What are the order pairs for -8x plus 3y equals -5 and 8x - 2y equals 6?
These are equations of two straight lines. Provided the equations are not of the same or parallel lines, there can be only one ordered pair. So the ordered pair is - not are : (0.5, -1)
Why cant equations of vertical lines be written in slope-intercept form but equations of horizontal lines can?
For vertical lines, when you try to figure out the slope, you get zero in the denominator - in other words, a division by zero.
Will equations of three parallel lines have value?
Yes. But for what?
What type of lines match these equations 3x plus 2y -5 -2x plus 3y -5?
If you mean 3x+2y = -5 and -2x+3y = -5 then they are straight line equations
When lines overlap in a system of equations?
Then they are simultaneous equations.
Which types of lines match these equations?
Invisible lines!
In geometrey what are two different equations that describe the same line Such lines are called coincident lines?
What do you call equations describing two or more lines
What are the order pairs for 2x plus y equals 1 and 2x - y equals -5?
These are equations of two straight lines. Provided the equations are not of the same or parallel lines, there can be only one ordered pair. So the answer is - (not are) : (-1, 3).
Which type of lines match these equations 4y plus 8x equals 20 y equals -2x plus 5?
The two equations represent the same straight line.
What is true about the lines represented by this system of linear equations?
That they, along with the equations, are invisible!
What are two equations for two lines that will intersect all the time?
They are simultaneous equations.
What are the order pairs for -8x plus 3y equals -5 and 8x - 2y equals 6?
These are equations of two straight lines. Provided the equations are not of the same or parallel lines, there can be only one ordered pair. So the ordered pair is - not are : (0.5, -1)
What is it called when you solve for two lines of algebraic equations simultaneousley?
Its called Simultaneous Equations
What types of lines would be the result of an inconsistent system of equation?
If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
