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Slopes and Equations of Lines

In Lesson 1.1, we explore the fundamentals of slopes and equations of lines. The lesson begins with plotting ordered pairs on a graph, demonstrating how to find coordinates for points like (4, -2) and (-5, 1). We define the x-intercept and y-intercept, emphasizing the concept of slope as the "steepness" of a line calculated by the change in y over the change in x. Various forms of line equations such as slope-intercept and point-slope are introduced. We also cover graphing techniques on the TI Calculator and discuss parallel and perpendicular lines with practical exercises.

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Slopes and Equations of Lines

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  1. Slopes and Equations of Lines Lesson 1.1

  2. The Plot Thickens • We plot ordered pairs (x-coord, y-coord) • Where would we plot (4, -2)? (2, 1) • (-5, 1) • (-1, -2) •

  3. x-intercept Line 'em Up • A line is a collection of points • When the x-coordinate is zero it intercepts the y-axis • When the y-coordinate is zero, it intercepts the x-axis y-intercept

  4. Slope of a Line • Represents the "steepness" of a line • Measured by the change in the y-value divided by the change in the x-value • (-3, 2) (3, 0)

  5. Equations of a Line • Slope-Intercept Form • Point-Slope Form

  6. Horizontal, Vertical Lines • Horizontal lines y = 12 • Note: slope is 0 • Vertical lines x = 7 • Note: slope is infinite, or "no slope"

  7. Graphing Lines on the TI Calculator • We wish to graph the equation • Go to the Y= screen – use ♦W or ♦F1 • Enter the function on the entry line • It appears in thelist

  8. Graphing Lines on the TI Calculator • Now specify the standard zoom F2 and 6 • Function will graph on axes

  9. Parallel and Perpendicular Lines • Parallel lines have the same slope • Perpendicular lines haveslopes that are negativereciprocals • Graph these to verify, use Zoom-Square

  10. Try It Out • Find the equation of a line through (2, -5) and parallel to y = 2x + 4 • Find the equation of a line with x-intercept of -2/3 and perpendicular to 2x – 3y = 5 • A business has sales of $27,000 in its 2nd year, $63,000 in 5th year. Let y be the sales for the xth year. Assume the data can be approximated by a st. line. Determine an equation for the sales • Use your answer to find out how many hears until sales surpass $100,000

  11. Assignment • Lesson 1.1 • Page 15 • Exercises 1 – 59 EOO, 61, 67, 75

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