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AP Calculus AB/BC

AP Calculus AB/BC. 1.1 Lines, p. 3. Lines and equations of lines are used in numerous business and economic applications. Linear functions are taught beginning with Algebra 1 and continuing all throughout Calculus.

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AP Calculus AB/BC

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  1. AP Calculus AB/BC 1.1 Lines, p. 3

  2. Lines and equations of lines are used in numerous business and economic applications. Linear functions are taught beginning with Algebra 1 and continuing all throughout Calculus. Our first definition in Calculus is “Increments”. An increment can be thought of something being added, or changed. In mathematics, an increment is the change in the x and y values from one point to another.

  3. Let’s take two arbitrary points on the coordinate plane as shown. = the change in x = run y = the change in y = rise So, the increments in the coordinates are: And, the slope of a line is defined as: x O If two lines are parallel, then they have the same slope (the slopes have the same values). If two lines are perpendicular, then the slopes are opposite (negative) reciprocals, and their product is negative one.

  4. Example 1 These increments can be used to find the slope of the line through points A and B.

  5. ▬▬Equations of Lines▬▬ m = slope y = mx + b Slope-Intercept: b= y-intercept Point-Slope: m = slope If (a, b) is a point in the coordinate plane, then x = a is a vertical line through (a, b), and y = b is a horizontal line through (a, b).

  6. This gives a y-intercept of 3 and a slope of Example 5 Find the slope and y-intercept and graph the line: 3x + 4y = 12 First, solve the equation for y. -3 +4

  7. y-intercept = 3 Slope = Now, it’s your turn. Find the slope and y-intercept, then graph the line

  8. Example The pressure p experienced by a diver underwater is related to the diver’s depth d by the equation of the form p = kd + 1 (k a constant). When d = 0 meters, the pressure is 1 atmosphere. The pressure at 100 meters is 10.94 atmospheres. Find the pressure at 50 meters. Here’s what we know: p

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