1 / 16

Understanding Line Slope and Equation Forms: From Basic Concepts to Applications

This guide covers essential concepts of line slopes, including defining slope, identifying vertical lines, and exploring the Point-Slope and Slope-Intercept forms of linear equations. It discusses the y-intercept and the different forms of line equations such as Standard, Point-Slope, and Slope-Intercept. The document explains graphing linear equations, solving them with calculators, and the relationships between parallel and perpendicular lines based on their slopes. It also includes practical applications like assessing the depreciation of a building over time.

yoshi
Download Presentation

Understanding Line Slope and Equation Forms: From Basic Concepts to Applications

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. Sect P-4 Lines in the Plane

  2. Slope of a line If the line is vertical, the slope is “undefined”

  3. Find the slope… • Passes through (-1,2) and (4,2)

  4. Point-Slope Form of the Line

  5. Find the Point-Slope Form • Line passes through (-3,-4) with a slope of 2

  6. Slope-Intercept Form • Y-intercept: the point where the line crosses (intersects) the y-axis • It will always cross at x=0. • y=mx + b m = slope of line b = the y value of the y-intercept of line… y-intercept is (0,b)

  7. Using the Slope-Intercept Form • Write the equation of the line with slope 3 that passes through (-1,6)

  8. Forms of the Equation of Lines • Standard Form: • Slope-Intercept: • Point-Slope: • Vertical Line: • Horizontal Line:

  9. Graphing Linear Equations • The “graph” is all pairs (x,y) that are solutions to the equation. • (2,1) is “one” solution to 2x + 3y = 8 • Substituting x=2 and y = 1 into the equation will give the answer 8. • There are infinitely many points on the graph.

  10. Graphing Linear Equations • Using Calculator • Solve the equation for y= • Enter into y= screen on calculator • Hit “graph” • Note: the graph window may need to be changed to view the parts needed.

  11. Parallel Lines • What do graphs of y = mx + b and y = mx + c have in common? How are they different?

  12. Perpendicular Lines • Graph y = 2x and y = - (1/2)x in a “square” viewing window. • Estimate the angle between the lines. • What can you say about the “slopes” of the two lines?

  13. Definitions… • Two non-vertical lines are “parallel” if and only if they have the same slope. • Two non-vertical lines are “perpendicular” if and only if their slopes m1 and m2 are “opposite reciprocals” of each other.

  14. Homework… P. 35 • Quick Review … 2,6,8 • Exercises …6, 10, 14, 18, 24, 34 (using calculator on 34 only)

  15. Find the Equation of Perpendicular Line • Given a line 4x + y = 3 • Find the equation of the perpendicular line that passes through (2,-3)

  16. Applying Linear Equations • Camelot Apartments purchased a $50,000 building and depreciates it (for tax purposes) $2000 per year over a 25 year period. • Write the equation showing the value of the building (for tax purposes) in terms of years after the purchase. • In how many years will the value be $24,500?

More Related