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1.4 Lines

1.4 Lines. Objectives: Find the slopes of lines, including parallel and perpendicular lines Graph lines Write the equations of lines, including horizontal and vertical lines. Example #1 Finding Slope from a Graph. Find the slope of each line shown below. L 1. L 2.

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1.4 Lines

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  1. 1.4 Lines Objectives: Find the slopes of lines, including parallel and perpendicular lines Graph lines Write the equations of lines, including horizontal and vertical lines

  2. Example #1Finding Slope from a Graph Find the slope of each line shown below. L1 L2 The slope is a ratio found by dividing the vertical “rise” by the horizontal “run”. L3 L4 L5

  3. Example #2Finding Slope Given Two Points Find the slope of the line that passes through (1,−2) and (4,1) Use the slope formula: Where Δy represents the change in y and Δx represents the change in x. Δy Δx

  4. Example #3Solving for a Variable Given Slope Find a number t such that the line passing through the two given points has a slope of −3. Set up a proportion. Cross multiply and solve for t.

  5. Example #4Slope-Intercept Form Find the slope and y-intercept of the following equation. Write the equation into slope-intercept form: The slope is then -14 and the y-intercept is 19. m is the slope and b is the y-intercept

  6. Example #5Graphing a Line Sketch the graph of , and confirm your sketch with a graphing calculator. Graph the line. Write the equation into slope-intercept form. Identify the slope and y-intercept.

  7. Example #6Writing the Equation of a Line Sketch the graph and find the equation of the line that passes through the point (−2,5) with slope −3. Write the equation in slope-intercept form. Method 1: Use the point-slope form

  8. Example #6Writing the Equation of a Line Sketch the graph and find the equation of the line that passes through the point (−2,5) with slope −3. Write the equation in slope-intercept form. Method 2: Use the slope-intercept form

  9. Example #6Writing the Equation of a Line Sketch the graph and find the equation of the line that passes through the point (−2,5) with slope −3. Write the equation in slope-intercept form. Graph:

  10. Example #7Linear Depreciation • An office buys a new color copier for $8000. Four years later its value is $2320. Assume that the copier depreciates linearly. • Write the equation that represents value as a function of years. OR

  11. Example #7Linear Depreciation • An office buys a new color copier for $8000. Four years later its value is $2320. Assume that the copier depreciates linearly. • Find its value three years after it was purchased, that is, the y-value when x = 3.

  12. Example #7Linear Depreciation • An office buys a new color copier for $8000. Four years later its value is $2320. Assume that the copier depreciates linearly. • Graph the equation.

  13. Example #7Linear Depreciation • An office buys a new color copier for $8000. Four years later its value is $2320. Assume that the copier depreciates linearly. • Find how many years before the system is worthless, that is, the x-value that corresponds to a y-value of 0.

  14. Example #8Equation of a Horizontal Line Describe and sketch the graph of the equation y = −2. Horizontal line with a slope of 0 which intercepts the y-axis at −2.

  15. Example #9Equation of a Vertical Line Find the equation of the vertical line shown below. Vertical lines have equations of the form x = a. Since this line crosses the x-axis at −3 the equation for this line is x = −3.

  16. Example #10Parallel and Perpendicular Lines • Identify whether the following lines are parallel, perpendicular, or neither, with the given equation. Since the two lines have the same slopes they are parallel.

  17. Example #10Parallel and Perpendicular Lines • Identify whether the following lines are parallel, perpendicular, or neither, with the given equation. Since the slopes are opposite reciprocals of each other then they are perpendicular.

  18. Example #10Parallel and Perpendicular Lines • Identify whether the following lines are parallel, perpendicular, or neither, with the given equation. Since the slopes are not the same nor are they opposite reciprocals of each other, then they are neither parallel or perpendicular.

  19. Example #11Parallel and Perpendicular Lines • Find the equation of the lines through the point (−4, 2) given the line M whose equation is shown below. • Parallel to M. For parallel lines use the same slope. Find the slope of line M. Write the equation of the line.

  20. Example #11Parallel and Perpendicular Lines • Find the equation of the lines through the point (−4, 2) given the line M whose equation is shown below. • Perpendicular to M. For perpendicular lines use slopes that are opposite reciprocals.

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