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| Tables and Graphs of Linear Equations |
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In the following questions, select “True” if the equation is linear or “False” if the equation is nonlinear.
To be a linear equation:
-There must be at least one variable, and at most 2 variables.
-The exponent with any of the variables must be equal to 1 (no more, no less).
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| 2) Linear? |
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| 4) Linear? |
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| In the following questions, decide if the data in the table represents a linear relationship between x and y. State T (True) if the relationship is linear and state the next ordered pair that would appear in the table. State F (False) for nonlinear relationships. |
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6) Linear? If true, what is the next ordered pair?
Hint: Notice there is a constant difference of 1 in the x-values. Look for a constant difference (other than 1 in this problem) in the y-values? The relationship is the same if that difference is the same throughout. |
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7) Linear? If true, what is the next ordered pair?
Hint: Check for constant differences in the x-values and the y-values. |
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8) Linear? If true, what is the next ordered pair?
Hint: Check for constant differences in the x-values and the y-values. |
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| 9) A book store charges a $6.00 membership fee and $3.00 for each book rented. In the graph, the x-axis represents the number of books rented and the y-axis represents the store's revenue. Select the correct data points for the graph. |
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| In the following problems, refer to the graph and data in the previous problem. |
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| Use this scenario to solve the following problems: Mathematics University plans to increase the enrollment capacity to keep up with an increasing number of student applicants. The college currently has an enrollment capacity of 2500 students and plans to increase its capacity by 75 students each year. |
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14) What linear equation could be used to find the enrollment capacity?
Hint: y = mx + b
slope (m) is the change in enrollment per year
y-intercept (b) is the initial enrollment |
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| 15) In the table about plant growth, what constant rate of change occurs? Explain what this rate of change means in terms of growth. |
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| 16) The graph shows the altitude of a skydiver after the parachute opens and s/he begins to descend. What is the rate of change and explain what the rate of change means in terms of the descent of the skydiver. |
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| 17) What is the average rate of change if a baby is 20 inches long at birth and 28 inches long at ten months? Label the answer with the correct units. |
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| In the following problems, find the slope of the line containing the indicated points. |
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In the following problems, identify the slope (m) and y-intercept (b) for the line that could be graphed for each given linear equation.
Hint: Write each equation in slope-intercept form first. y = mx + b |
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| 21) What is the slope and y-intercept for the linear equation, y + 2x = 0? |
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| 22) What is the slope and y-intercept for the linear equation, 2x = 8 + 4y? |
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| Use this scenario to solve the following problems: Ryan buys a computer system for $3800. For tax purposes, he declares a linear depreciation (loss of value) of $400 per year. Let y be the declared value of the computer after x years. |
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| Linear Equations in Two Variables |
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| 27) What is the equation of a line that has a slope of –1/2 and contains the point (8, 1)? Express the equation in slope-intercept form, y = mx + b. |
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| 28) What is the equation of a line that has a slope of –3 and contains the point, (6, –5)? Express the equation in slope-intercept form, y = mx + b. |
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In the following problems, express the equations in slope-intercept form, y = mx + b.
Hint: Find the slope, then use the point-slope formula to find the equation. |
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| 29) What is the equation of a line that contains the points (1, –3) and (3, –5)? |
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| 30) What is the equation of a line that contains the points (8, –3) and (–8, 3)? |
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| Equations of Horizontal and Vertical Lines |
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| In the following problems, identify the slope (m) and y-intercept (b) for the line that can be graphed for each given linear equation. |
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| 31) What is the slope and y-intercept for the equation, y = –2? |
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| 32) What is the slope and y-intercept for the equation, x = 3? |
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| Parallel and Perpendicular Lines |
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In the following problems, find an equation for a line that contains the given point and is PARALLEL to the given equation. Express the equation in slope-intercept form.
To enter non-standard keyboard characters for equations with fractions, follow the examples shown below. |
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In the following problems, find an equation for a line that contains the given point and is PERPENDICULAR to the given equation. Express the equation in slope-intercept form.
Hint: To find the slope of a perpendicular line find the opposite reciprocal of the slope of the given line; that is, write the slope as a fraction, flip it, and add on a negative sign. |
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| 37) What does the slope of a line indicate about the line? |
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38) What is the y-intercept for lines that have the general form, y = mx?
For example, what would be the y-intercepts for equations such as y = 4x or y = –3x? If necessary, graph the sample equations to see what their y-intercepts are. |
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| 39) Explain the difference between a line with a slope of 0 and a line with no slope. |
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| 40) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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