MATHCP Geometry  - Unit 30: Graphing Equations of Lines
Linear Equations

1) True or False. In a two-dimensional coordinate plane, the graphs of linear equations will be straight lines.

2) Which statement is true for the standard form of a linear equation?

3) Write the equation shown below in standard form. Adjust the equation, if necessary, to make the leading coefficient (the coefficient of the first term) positive.

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4) Write the equation shown below in standard form and without fractions. Adjust the equation, if necessary, to make the leading coefficient (the coefficient of the first term) positive.

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5) Which equation is linear? State the letter of the linear equation.

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6) Which equation is NOT linear? State the letter of the correct answer.

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7) True or False. The graph shown below represents a linear equation.

8) The equation shown below is written in standard form. Which equation could have been the original equation? State the letter of the correct answer.

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Slopes and Intercepts

9) The slope of a line refers to what characteristics of a line?

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10) Fill in the missing parts of the general ratio that describes the slope of a line.

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11) Which statement is true about the slopes of the lines graphed below?

12) Which of the formulas is used to determine the slope of a line? State the letter of the correct answer.

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13) What is the slope of a line going through the points (2, 7) and (–5, –9)?

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14) Select the phrase that completes the following statement about Theorem 30: If an equation of a line is written in slope-intercept form (y = mx + b), then ...

15) Write the equation, –4x + y = –8, in slope-intercept form, and then graph the equation. State (a) the slope-intercept form, (b) the location of the y-intercept, and (c) the slope. (To print out the graph paper provided below, right-click and print picture.)

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16) Graph the equation, x + 2y = 6 by finding the x-intercept and the y-intercept. State (a) the location of the x-intercept, (b) the location of the y-intercept, and (c) the slope. (To print out the graph paper provided below, right-click and print picture.)

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17) For the given graph, state (a) the type of slope the line has, (b) the location of the x-intercept, (c) the location of the y-intercept, and (d) the slope. (Each line on the graph represents one unit.)

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18) On graph paper, graph the equation, 4x + 3y = 15. State the (a) slope, (b) x-intercept, and (c) y-intercept?

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Point-Slope Form

19) Which equation represents the point-slope form? State the letter of the correct answer.

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20) Use the point-slope form to write the equation of a line that contains the point and slope given below. Express the equation in slope-intercept form.

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21) Use the point-slope form to write the equation of a line that contains the points (8, 3) and (9, 6). Express the equation in slope-intercept form. (Hint: First, determine the slope of the line using the slope formula.)

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22) Refer to the equation given below and fill in the missing coordinates. (a) What are the six ordered pairs displayed in the table that could be used to graph the equation? (b) What is the slope of the line that represents the equation? (Hint: The equation may be easier to solve by first multiplying both sides by 3 to write an equivalent equation without a fraction.)

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23) The following points are collinear: A(2,19), B(1, 11) and C(–1,–5). Use points A and B to determine the slope and the equation of the line that includes all three points. (a) State the linear equation for the line in slope-intercept form. (b) Explain how to prove that point C is also a point on the line.

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24) Use triangle NOP, N(–4, –1), O(5, 4), and P(3, –4), to determine the equation for a line that is a median of the triangle and is drawn from point N to segment OP, and then answer the following questions: (a) What are the coordinates of the midpoint of segment OP? (b) What is the equation of the median? Write the equation in slope-intercept form.

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Equations of Horizontal and Vertical Lines

25) Complete the following statements: (a) The slope of a horizontal line is __________. (b) The slope of a vertical line is __________.

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26) Answer the following questions about the graph shown below: (a) All of the points on the graphed line have a y-coordinate that is equal to what value? (b) What is the equation of the line? (Note: Each line represents one (1) unit.)

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27) Answer the following questions about the graph shown below: (a) All of the points on the graphed line have an x-coordinate that is equal to what value? (b) What is the equation of the line? (Note: Each line represents one (1) unit.)

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28) Which graph displays the equation, y = 4? State the letter of the correct answer.

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29) Which graph displays the equation, x = –5? State the letter of the correct answer.

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30) The equation, y = 2, and the coordinates for two points on the line are shown below. (a) What is the slope of the line? (b) Explain how to calculate the slope by using the two points given.

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31) The equation, x = 2, and the coordinates for two points on the line are shown below. (a) What is the slope of the line? (b) Explain how to calculate the slope by using the two points given.

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32) Do the parallel lines shown below have the same slope? If so, then state “yes” and give the slope. If the slopes are different, then state “no” and give both slopes.

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Parallel and Perpendicular Lines

33) Complete the following statements: Parallel lines have the __________ slope. Perpendicular lines have slopes that are __________ __________.

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34) The graphs of the lines of the equations given below are __________ lines.

35) For the equations shown below, the product of the slopes is ____ and the graphs of the lines are __________.

36) Which equation represents a line that is parallel to y = 3x + 5 and passes through the point (–2, 8)?

37) Which equation represents a line that is perpendicular to the line represented by 8x + 3y = 6 and passes through point (6, –2)? State the letter of the correct answer.

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38) Refer to triangle JKL to answer the following questions: (a) What is the slope of segment JL? (b) What is the slope of altitude KM? (c) What is the equation that represents the altitude?

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39) Are lines "a" and "b" parallel? Explain, through slopes, how you derived the answer.

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40) Are lines "c" and "d" perpendicular? Explain, through slopes, how you derived the answer.

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Determine, through slopes, what kind of quadrilateral is graphed below, and then answer the next three questions.

41) What are the slopes of (a) segment QR, (b) segment TS, (c) segment RS, and (d) segment QT?

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42) Answer the following questions: (a) What is the slope of diagonal QS? (b) What is the slope of diagonal RT? (c) Segment QR and segment RT form what kind of lines?

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43) What kind of quadrilateral is QRST?

Use, Create, and Interpret Scatter Plots

44) Answer the following questions about the scatter plots shown below: (a) Which scatter plot shows a positive correlation in the data? (b) Which scatter plot shows a negative correlation in the data? (c) Which scatter plot shows no correlation in the data?

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45) True or False. In a scatter plot, the "line of best fit" must pass through all the points.

The following table shows the national average of the math SAT scores for students entering college classes from 1993 through 2002. Print out the table and grid, and then make a scatter plot. Upon completion of the scatter plot, draw a "line of best fit" and then answer the next three questions.

46) Select the meaning of the slope of the "line of best fit” in the graph.

47) Select two points that your “line of best fit” passes through and calculate the slope of the “line of best fit”. Then write the equation of the “line of best fit”. (a) What is the slope of YOUR “line of best fit”? (b)What were the two points that you used to determine the slope?

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48) Select an equation that is close to the equation that you determined in the previous problem. State the letter of the correct answer. (Note: “x” represents the year of the SAT test and “y” represents the average score of the SAT test.)

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49) Use the equation of the "line of best fit” to estimate the national average math SAT test score (a) for 2003 and (b) for 2004.

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Extended Research: Check with your instructor to see if he/she is interested in awarding extra credit to you for writing a one-page report on the following research topic: Since the actual 2003 and 2004 national average math SAT scores are already compiled, do an Internet search and find out the actual results. What are the actual results of the national math SAT scores for the years 2003 and 2004? Compare your “predicted” scores with the actual scores. How does the trend of the actual data compare to the “predicted” scores? Predict what the SAT scores will be in 2060. Justify your prediction based in mathematics, in actual results, and some common sense. You may include graphs and actual data in your report. Be sure to include a list of websites that you referenced when writing the report.

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