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Notes
Problems
Find the net change between these 2 points.
\(\textbf{1)}\) \( (3,4) \) and \( (8,16) \)
\(\textbf{2)}\) \( (1,-3) \) and \( (4,6) \)
\(\textbf{3)}\) \( (-2,-2) \) and \( (8,8) \)
\(\textbf{4)}\) \( (4,7) \) and \( (8,12) \)
\(\textbf{5)}\) \( f(x)=3x+2 \) from \( x=1 \) to \( x=4 \)
\(\textbf{6)}\) \( f(x)=x^{2}+3 \) from \( x=2 \) to \( x=3 \)
See Related Pages\(\)
\(\bullet\text{ Graphing Linear Equations}\)
\(\,\,\,\,\,\,\,\,2x-3y=6 \) 
\(\bullet\text{ Slope Formula}\)
\(\,\,\,\,\,\,\,\,m=\frac{y_2-y_1}{x_2-x_1}\)
\(\bullet\text{ Slope Intercept Form}\)
\(\,\,\,\,\,\,\,\,y=mx+b\)
\(\bullet\text{ Point Slope Form}\)
\(\,\,\,\,\,\,\,\,y-y_1=m(x-x_1)\)
\(\bullet\text{ Parallel and Perpendicular Slope}\)
\(\,\,\,\,\,\,\,\,m_1=m+2,\,\,\,m_1=\frac{1}{m_2}\)
\(\bullet\text{ Distance Between a Point and a Line}\)
\(\,\,\,\,\,\,\,\,(3,4) \text{ and } y=\frac{3}{4}x−2\)
\(\bullet\text{ Finding x- and y- intercepts}\)
\(\,\,\,\,\,\,\,\,y=2x+4\)
In Summary
The net change is the overall difference between the initial value and the final value of a quantity. It is calculated by subtracting the initial value from the final value. The net change is a useful concept in mathematics because it allows us to quickly find the overall change in a quantity without having to calculate the individual changes along the way.
Net change is typically covered in a high school algebra or precalculus class.
Net change has many real-world applications. For example, it can be used to measure the overall change in a stock’s price over time, the overall change in a person’s weight over a period of weeks or months, or the overall change in the temperature of a substance over time.
The concept of net change was first used by the ancient Greek mathematician Archimedes, who used it to measure the overall change in the amount of water displaced by an object.
Net change is closely related to slope. In the numerator of the slope formula you use the net change of your two points.
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