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Linear Equations
Intercepts
Slope
Sequences
Mystery
100
State the standard form of a linear equation.
What is Ax + By = C
100
Find the x and y intercepts of the equation: y = 3x - 6
What is x = 2, y = -6.
100
Find the slope of the line that passes through the pair of points: (-5,3), (-5,9).
What is Undefined slope.
100
The difference between successive terms of an arithemtic sequence is the constant of variation. True or False. If false, please provide the correct difference between successive terms of an aritmetic sequence.
What is false, that would be the common difference.
100
Find the root (solution) of the equation. 4x - 24 = 0
What is x = 6.
200
Determine whether the equation is linear. If it is, write the equation in standard form. y = -4x + 3
What is yes. 4x + y = 3
200
Find the intercepts of the equation: y = -2x
What is x = 0, y = 0.
200
When driving up a certain hill, you rise 15 feet for every 1000 feet you drive forward. What is the slope of the road? Is this a steep road?
What is 3/200. No, this is not a steep road.
200
Determine if the sequence is arithmetic: -3, 1, 5, 9, ...
What is yes, this is arithmetic.
200
The first four terms of an arithmetic sequence are 28, 20, 12, and 4. Which term of the sequence is -36?
What is the 9th term. a sub n = a sub 1 + (n-1)d -36 = 28 + (n-1)(-8) -36 = 28 + -8n + 8 -36 = -8n + 36 -72 = -8n 9 = n
300
Determine whether the equation is linear. If it is, write the equation in standard form. xy + 3y = 8
What is no, this is not linear.
300
The function y = -15 + 3x represents the outside temperature, in Farenheit, in a small Alaskan town where x represents the number of hours after midnight. The function is accurate for x values representing midnight through 4:00 pm. Find the zero of this function.
What is x = 5. (The zero of a function represents the x intercept.)
300
Find the value of r so the line that passes through the pair of points has the given slope. (12,10), (-2,r), m = -4
What is r = 66.
300
Write an equation for the nth term of the arithmetic sequence: -2, 3, 8, 13
What is a sub n = -2 + (n-1)5 a sub n = -2 + 5n - 5 a sub n = 5n - 7
300
Find the slope of the graph. (see graph)
What is -1/2.
400
Find the root (solution) of the equation: 18 + 8x = 0.
What is x = -9/4.
400
An amusement park charges $50 for admission before 6pm and $20 for admission after 6pm. On Saturday, the park took in a total of $20,000. Let x represent the admissions before 6 and let y represent the admissions after 6. Write an equation, graph the equation, and find the x and y intercepts.
What is 50x + 20y = 20,000. The x = 4,000 and y = 1,000. See graph.
400
Find the value of r so the line that passes through the points has the given slope. (04,8), (r,12), m = 4/3
What is r = -1
400
What would the 15th term of the following arithmetic sequence be? 28, 25, 22, 19, ...
What is -14. Remember use the formula: a sub 15 = 28 + (15-1)(-3) a sub 15 = 28 + 14(-3) a sub 15 = 28 - 42 a sub 15 = -14
400
Find the slope of the line passing through the points: (5,-3), (-2, -3)
What is zero slope.
500
For her birthday, Jen receives a $50 gift card to download songs. The function m = -0.50d + 50 represents the amount of money that remains on the card after a number of songs d are downloaded. Find the zero and explain what it means in the context of this situation.
What is x (or d) = 100. Remember the zero of a function is the x intercept when y = 0. This means that at 100 songs there will be a $0 balance on the card.
500
The equation 5x + 12y = 240 describes the total amount of money collected when selling x paperback books at $5 per book and y hardbacks at $12 per book. Graph the equation using the x and y intercepts.
What is x = 48, y = 20. (See graph)
500
Find the slope of the line that passes through the pair of points. (1/3, 3/4), (2/3, 1/4)
What is m = -3/2
500
The fourth term of an arithmetic sequence is 8. If the common difference is 2, what is the first term?
What is 2. a sub n = a sub 1 + (n-1)(d) a sub 4 (which is 8) = (a sub 1) + (4-1)(2) 8 = a sub 1 + 3(2) 8 = a sub 1 + 6 2 = a sub 1
500
A jacket originally costed $125. The sale price is $99. What is the percent of decrease? Round to the nearest percent. You must round correctly.
What is about 21%