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This is the first fundemental theorem of Calculus. The slope of a line is very important in your first calculus course. The slope tells you the rate of change. This means how much is the object change in height compared to its change in length. The slope of a line in Calculus is used as the first derivative. If you can take the slope of a line at one particular point you will find the answer to the derivative at this point.
Remember this. You first equation on your graph is called your position equation. If you take the derivative of this equation it is called the velocity equation. The velocity equation is how much the position equation is sloping at each point. If you take the derivative of the velocity equation you will get the acceleration equation. The accerelation equation is how much the velocity is sloping at each point. You can take the derivative of the acceleration equation and this will give you the jerk equation. The jerk equation is not used in many applications and I have never used this equation in any of my 4 calculus classes.
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Determine whether the graphs of the equations are parallelperpendicular or neither?
Base on the slope of two linear equations (form: y = mx+b, where slope is m): - If slopes are equal, the 2 graphs are parallel - If the product of two slopes equals to -1, the 2 graphs are perpendicular. If none of the above, then the 2 graphs are neither parallel nor perpendicular.
Does in linear graphs the slope of the line change with the x coordinate?
In a linear graph the slope is the same everywhere, assuming vertical line graphs are not allowed. Depending on context, a vertical line (say x = 3) is not always allowed. If the graph is a vertical line then the slope is infinite at the single value of x. (That would be 3 in the example above.) The slope would then be undefined elsewhere.
Difference between the graphs of linear equations and a direct variation?
Linear has a slope direct does not but both go through the orgin
The graph of a system of equations with the same slope will have no solutions?
That's right. If a system of equations has a solution, then their graphs intersect, and the point where they intersect is the solution, because it's the point that satisfies each equation in the system. Straight-line graphs with the same slope are parallel lines, and they never intersect, which is another way of saying they have no solution.
When solving systems of linear equation's when would you get no solution as an answer?
You get no solution if the lines representing the graphs of both equations have the same slope, i.e. they're parallel. "No solution" is NOT an answer.
Does in linear graphs the slope of the line change with the x-coordinate?
No. A linear graph has the same slope anywhere.
Determine whether the graphs of the equations are parallelperpendicular or neither?
Base on the slope of two linear equations (form: y = mx+b, where slope is m): - If slopes are equal, the 2 graphs are parallel - If the product of two slopes equals to -1, the 2 graphs are perpendicular. If none of the above, then the 2 graphs are neither parallel nor perpendicular.
What is physical meaning of slope for voltages vs current graphs?
The slope of a voltage vs. current graph represents the resistance in the circuit. It indicates how the voltage changes with respect to the current flowing through the circuit. A steeper slope indicates higher resistance, while a shallower slope indicates lower resistance.
Does in linear graphs the slope of the line change with the x coordinate?
In a linear graph the slope is the same everywhere, assuming vertical line graphs are not allowed. Depending on context, a vertical line (say x = 3) is not always allowed. If the graph is a vertical line then the slope is infinite at the single value of x. (That would be 3 in the example above.) The slope would then be undefined elsewhere.
Does the steepness of motion graphs slope depend on how quickly or slowly the object is moving?
No, it depends on radial acceleration.
How do you interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
How do you recognize acceleration graphs?
Acceleration graphs show changes in velocity over time. A positive slope indicates speeding up, a negative slope indicates slowing down, and a horizontal line indicates constant velocity. The steeper the slope, the greater the acceleration.
How do you do equations and graphs for slope?
The equation for the slope between the points A = (x1, y1) and B = (x2, y2) = (y2 - y1)/(x2 - x1), provided x1 is different from x2. If x1 and x2 are the same then the slope is not defined.
What does the m in algebra stand for?
If you are talking about linear graphs, m refers to the gradient (aka slope or rate of change).
What does m represent in your equation?
If you are talking about linear graphs, m refers to the gradient (aka slope or rate of change).
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
Is the following sentence true or false the steepness of a motion graphs slope depends on how quickly or slowly the object is moving?
true
