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How do you know if the equation is a direct variation?
When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation. y=2x is direct variation y=x+2 is not direct variation
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
What is direct square variation in math?
direct square variation is a function that relates the same or equal constant ratio. It is a function that is typically used in different kinds of algebra.
What is the relationship between the equations of parallel lines?
They have the same slope. If you write the lines in the slope-intercept form, you will get, for each line: y = ax + b where a is the slope, and b is the y-intercept (where the line crosses the y-axis). For two or more parallel lines, the coefficient "a" will be the same.
Can systems of equations with the same slopes have infinitely many solutions?
Absolutely, but only if they're concurrent. This means that they not only share the same slope, but also share the same y-intercept, which results in the lines sharing every x-y coordinate. Concurrent is another way of saying the lines are actually just the same line. If they're not concurrent, then they're only parallel, so will have no solutions. For example:Our system:2x + 3y = 64x + 6y = 12These two equations, when you put them in slope-intercept form, will have the same slope and the same y-intercept. This means they are concurrent, and their system will have infinitely many solutions. Notice that if you multiply the entire first equation by 2, you get the second equation. Concurrent lines always share this kind of relationship, where you can multiply one by some number to get the other.Another system:2x + 3y = 64x + 6y = 10These two equations, when you put them in slope-intercept form, will have the same slope but will not have the same y-intercept. This means they are parallel, so their system will have no solutions. Notice that if you multiply the entire first equation by 2, the coefficients on x and y will be the same in both equations, but the constants on the right side will not. This relationship is shared by all parallel lines.
Is the constant of variation the same as slope?
yes y=kx is the formula for direct variation, and k represents constant of variation which can also be called slope.
How can we tell if two lines are parallel perpendicular or neither just from their equations?
If the slope of the equations are the same then they are parallel If the slope of the equations are minus reciprocal then they are perpendicular If the slope of the equations are different then they are neither
The graph of a system of equations with the same slope and the same y intercepts will have no solution?
The statement - The graph of a system of equations with the same slope and the same y intercepts will have no solution is True
Is The graph of a system of equations with the same slope will have no solutions?
Yes.
How can you tell if two equations are parallel?
if they have the same slope If two linear equations are inconsistent - that is, have no solution, then the graphs would be parallel and have the same slope if their slope is defined. Example: x + y = 1 x + y = 2 Example with no slope: x = 1 x = 2
Set of the equations graphed on the same grid is said to be?
Collinear slope.
How do you know if the equation is a direct variation?
When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation. y=2x is direct variation y=x+2 is not direct variation
What is a direct variation?
A direct variation is when the value of K in multiple proportions is all divisible by the same number for example: XY=(1)(10) K=10 XY=(2)(20) K=40 XY=(3)(30) K=90 XY=(4)(40) K=160 In this situation the constant (K) of each proportion is divisible by 10 making the multiple equations a direct variation.
In a table if the ratios weren't equivalent would it still be direct variation?
No; each ratio has to be the same for a direct variation.
Is it possible to have two different looking equations in the same version of point slope form for the same line?
It depends on what constitutes different looking: how similar must the equations be before you see that they are the same. If both equations are in the point-slope form, the coefficients of one equation must be a fixed multiple of the coefficients of the other.
By looking at two linear equations how can you tell that the corresponding lines are parallel?
By looking st two linear equations you can tell that the corresponding lines are parallel when the slope is the same. The slope controls where the line is.
If the graphs of two linear equations in a system have the same slope the system has what kind of solution?
If they have the same slope, then there are two possibilities. First say they have the same slope and different y intercepts. This means they are parallel lines and there is no intersection. The solution is the empty set or we say there is no solution.If the y intercept is the same, then the two equations represent the same line. In this case there is an infinite number of solutions.
