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Chapter P: Prerequisite Information

Chapter P: Prerequisite Information. Section P-4: Lines in the Coordinate Plane. Objectives. You will learn about: Slope of a line Point-slope form equation of a line Slope-intercept form equation of a line Graphing linear equations in two variables Parallel and perpendicular lines

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Chapter P: Prerequisite Information

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  1. Chapter P:Prerequisite Information

    Section P-4: Lines in the Coordinate Plane
  2. Objectives You will learn about: Slope of a line Point-slope form equation of a line Slope-intercept form equation of a line Graphing linear equations in two variables Parallel and perpendicular lines Applying linear equations in two variables Why: Linear equations are used extensively in applications involving business and behavioral science.
  3. Vocabulary Slope Point-slope form y-intercept Slope-intercept form General form Linear equation in x and y Graph Solution x-intercept Viewing window
  4. Slope of a Line The slope of the non-vertical line through the points (x1,y1) and (x2,y2) is:___________. If the line is vertical, then the slope is undefined.
  5. Example 1:Finding the Slope of a Line Find the slope of the line through the two points. Sketch a graph of the line. (-1, 2) and (4, -2) (1, 1) and (3, 4)
  6. Point-Slope Form of an Equation of a Line The point-slope form of an equation of a line that passes through the point (x1,y1) and has a slope m is:___________________.
  7. Example 2:Using Point-Slope Form Use the point-slope form to find an equation of the line that passes through the point (-3, -4) and has slope 2. Express your answer in slope-intercept form.
  8. Slope-Intercept Form of an Equation of a Line The slope-intercept form of an equation of a line with slope m and y-intercept (0, b) is:_________________.
  9. Example 3:Using the Slope-Intercept Form Write an equation of the line with slope 3 that passes through the point (-1, 6) using slope-intercept form.
  10. Forms of Equations of Lines General Form: Ax + By + C = 0, where A and B are both not zero (one may be zero, just not both) Slope-Intercept Form: y = mx + b Point-Slope Form: y - y1= m(x - x1) Vertical Line: x = a (The slope is undefined) Horizontal Line: y = b (The slope is zero)
  11. Example 4:Using a Graphing Utility Draw the graph of 2x + 3y = 6. On graphing calculator: Convert to slope-intercept form. Type the equation in the y = function Select an appropriate window (the default window will work) Hit graph.
  12. Parallel and Perpendicular Lines Two non-vertical lines are parallel if and only if their slopes are equal. Two non-vertical lines are perpendicular if and only if their slopes m1 and m2 are opposite reciprocals.
  13. Example 5:Finding an Equation of a Parallel Line Find an equation of the line through point P(1, -2) that is parallel to the line L with the equation 3x – 2y = 1
  14. Example 6:Finding an Equation of a Perpendicular Line Find an equation of the line through point P(2, -3) that is perpendicular to the line L with the equation 4x + y = 3.
  15. Example 7:Finding the Depreciation of Real Estate Camelot Apartments purchased a $50,000 building and depreciates it $2000 per year over a 25 year period. Write a linear equation giving the value y of the building in terms of the years x after the purchase. In how many years will the building be $24,500?
  16. Example 8:Finding a Linear Model for Americans’ Personal Income
  17. Example 8(Continued) Write a linear equation for Americans’ income y in terms of the year x. (use the data for 1998 and 1999 for the equation). Use the equation to estimate Americans’ income in 2001. Use the equation to estimate American’s income in 2006.
  18. Example 8(Continued) Graph the scatter plot of the data. On Graphing Calculator: Step 1: Enter the years in List 1 and the income in List 2 Step 2: Use the “Stat Plot” key (2nd, y =); select “on” and “scatter plot” Step 3: x-list (L1) and y-list (L2)—this may already be done as the default setting. Step 4: Select an appropriate window Step 5: Find the linear regression line: STAT CALC Option #4 ENTER Step 6: On your main screen, you should see: LinReg y=ax + b a=0.36 b=-711.78 Step 7: graph the linear regression line.
  19. Problem: Assume that the speed of light is approximately 186, 000 miles per second. Answer the following: If the distance from the Moon to the Earth is approximately 237,000 miles, find the length of time required for light to travel from the Earth to the Moon. If light travels from the Earth to the Sun in 8.32 minutes, approximate the distance from the Earth to the Sun. If it takes 5 hours and 29 minutes for light to travel from the Sun to Pluto, approximate the distance from the Sun to Pluto.
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