rates of change and writing linear equations - weebly
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Honors Calculus
Keeper 3
The average rate of change between any two points on the graph of ๐ is the slope of the line through those points.
The average rate of change on the interval [๐๐, ๐๐] is
๐ =๐ ๐๐ โ ๐(๐๐)
๐๐ โ ๐๐
p. 4
1. Find the average rate of change of ๐ ๐ฅ = โ๐ฅ3 + 3๐ฅ on each interval:
a. โ2,โ1
b. [0,1]
2. Find the average rate if change on the interval [โ6,2].
๐ ๐ฅ =๐ฅ + 5
๐ฅ โ 4
3. Find the average rate if change on the interval [โ4,4].
๐ ๐ฅ = ๐ฅ + 8
Slope-Intercept Form: Given the slope ๐ and the ๐ฆ-intercept ๐,
๐ฆ = ๐๐ฅ + ๐
Point-Slope Form: Given the slope ๐ and a point (๐ฅ1, ๐ฆ1)
๐ฆ โ ๐ฆ1 = ๐ ๐ฅ โ ๐ฅ1
Standard Form: ๐๐ฑ + ๐๐ฒ = ๐
p. 5
1. Write the equation of the line that passes
through (2,3) and has a slope of โ1
2.
2. Write the equation of the line that passes through (3,2) and is perpendicular to the line ๐ฆ = โ3๐ฅ + 2
3. Write the equation of the line that passes through (3,2) and is parallel to the line ๐ฆ = โ3๐ฅ + 2
4. Write the equation of the line that passes through (โ2,โ1) and (3,4).
5. Find the standard form of the equations of the lines that pass through the point (2, โ1) and is perpendicular to the line 2๐ฅ โ 3๐ฆ = 5