1 / 18

PreCalculus

PreCalculus. 1.2 – Linear Equations in Two Variables. Using Slope. The simplest mathematical model for relating two variables is the linear equation in two variables y = mx + b (slope intercept form), where m represents the slope and b represents the y-intercept.

solada
Download Presentation

PreCalculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PreCalculus 1.2 – Linear Equations in Two Variables

  2. Using Slope • The simplest mathematical model for relating two variables is the linear equation in two variables y = mx + b (slope intercept form), where m represents the slope and b represents the y-intercept. The slope of a nonvertical line is the number of units the line rises (or falls) vertically for each unit of horizontal change from left to right

  3. Example 1 – Sketching Lines Sketch the lines through the point with the indicated slopes. • Point: (3, 2) Slope: ½ • Point: (-1, 3) Slope: -2

  4. Example 2 – Graphing a Linear Equation Sketch the graph of each linear equation: A) y = 2x + 1 B) y = 2 • x + 2y = 4 D) x + 2 = -1

  5. Example 3 – Using Slope as a Ratio The maximum recommended slope of a wheelchair ramp is 1/12. A business is installing a wheelchair that rises 22 inches over a horizontal length of 24 feet. Is the ramp steeper than recommended?

  6. Example 4 – Using Slope as a Rate of Change A kitchen appliance manufacturing company determines that the total cost in dollars of producing x units of a blender is C = 25x + 3500 (cost equation). Describe the practical significance of the y-intercept and slope of this line.

  7. Finding the Slope of a Line Slope = Slope = Slope =

  8. Example 5 – Finding the Slope of a Line Through Two Points Find the slope of the line passing through each pair of points: • (-2, 0) and (3, 1) (b) (-1, 2) and (2, 2) • (0, 4) and (1, -1) (d) (3, 4) and (3, 1)

  9. Example 6 – Using the Slope-Intecept Form Find the slope-intercept form of the equation of the line that has a slope of 3 and passes through the point (1, -2).

  10. Example 7 – Equation of a Line through Two Points Find the slope-intercept form of the equation of the line passing through the points (2, 4) & (-1, 5).

  11. Example 8 – Predicting Revenue per Share The revenue per share for eBay Inc. was $0.20 in 1998 and $0.91 in 1999. Using only this information, write a linear equation that gives the revenue per share in terms of the year. Then predict the revenue per share for 2000.

  12. Extrapolation • The prediction method in example 8 is called linear extrapolation. Extrapolation occurs when a predicted point is outside the range of the two given points.

  13. Interpolation • Interpolation occurs when a predicted point is inside the range of the two given points.

  14. Equations of Lines General Form: Ax + By + C = 0 Vertical Line x = a (where a is the x-intercept) Horizontal line: x = b Slope-Intercept Form: y = mx + b

  15. Parallel & Perpendicular Lines • Two distinct non-vertical lines are parallel if and only if their slopes are equal. Example: y = 2x + 3 & y = 2x – 4 are parallel lines • Two non-vertical lines are perpendicular if and only if their slopes are negative reciprocals of each other. • Example: y = -½x – 1 & y = 2x + 3 are perpendicular lines

  16. Example 9 – Finding Parallel and Perpendicular Lines Find the slope-intercept forms of the equation of the lines that pass through the point (2, -1) and are (a) parallel to and (b) perpendicular to the line 2x – 3y = 6.

  17. Example 10 – Straight Line Depreciation Your publishing company has purchased a $12,000 machine that has a useful life of 8 years. The salvage value at the end of 8 years is $2000. Write a linear equation that describes the book value of the machine each year.

More Related