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The change in ( y ) over the change in ( x ) represents the slope of a line in a Cartesian coordinate system. It quantifies how much ( y ) increases or decreases as ( x ) changes, indicating the rate of change between the two variables. This concept is fundamental in calculus and is often used in analyzing linear relationships in mathematics and various applied fields.
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What is the equation of a line in standard form?
The standard form equation of a line is y=mx+b. M represents the slope; slope is the change in x over the change in y. B represents the y-intercept.
What does slope represent?
In math, the slope of a line represents its steepness. It is the change in y values over the change in the values of x, or rise over run.
The change in y over the change in x?
the change in y over the change in x equals the slope(m) in the equation y=mx+b
What does the slope tell you about changes in x and y?
slope is change in y over change in x
Does slope equals change in y change in x?
yes, change in y over change in x equals slope
What is the equation of a line in standard form?
The standard form equation of a line is y=mx+b. M represents the slope; slope is the change in x over the change in y. B represents the y-intercept.
What does slope represent?
In math, the slope of a line represents its steepness. It is the change in y values over the change in the values of x, or rise over run.
The change in y's over the change in x's?
the change in y over the change in x equals the slope(m) in the equation y=mx+b
The change in y over the change in x?
the change in y over the change in x equals the slope(m) in the equation y=mx+b
What is the delta in mathematics?
Delta is a symbol used in mathematics and science that represents change. For example, delta y over delta x means the change in y over the change in x.
What does the slope tell you about changes in x and y?
slope is change in y over change in x
Does slope equals change in y change in x?
yes, change in y over change in x equals slope
What is the steepness of a line on a graph represents?
The change in the y-value over the x-value, the slope, m, (y1-y2)/(x1-x2).
What does slope tell you about change x and y?
The slope of a line represents the rate of change between the dependent variable (y) and the independent variable (x). Specifically, it indicates how much y changes for a unit change in x; a positive slope means y increases as x increases, while a negative slope indicates that y decreases as x increases. The steeper the slope, the greater the rate of change. Slope can also be interpreted as the average rate of change over the interval being considered.
How do you find the rate of change between ordered pairs?
To find the rate of change between ordered pairs, you calculate the difference in the y-values (output) and divide it by the difference in the x-values (input). This is expressed as the formula: Rate of Change = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the two ordered pairs. The result represents how much y changes for a unit change in x.
This is flipping an image over the x-axis. The coordinates change from (x y) to (x -y).?
Yes, they do.
What is the slope of a function?
The slope of a function is the y-intercept or the change in y, over the change in x.
