Linear Functions
Practice interpreting slope, intercepts, and linear function notation.
25 questions
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If f(x) = x + 7 and g(x) = 7x, what is the value of 4f(2) − g(2)?
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The y-intercept of the graph of y = −6x − 32 in the xy-plane is (0, y). What is the value of y?
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Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is 63 inches. The equation 3x + 6y = 63 represents this situation, where x is the number of sides of figure A and y is the number of sides of figure B. Which statement is the best interpretation of 6 in this context?
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The function f is defined by the equation f(x) = 7x + 2. What is the value of f(x) when x = 4?
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A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents this situation, where x represents the number of 1-point questions and y represents the number of 3-point questions?
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A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934. The equation 2x + 35y = 3,934 represents this situation. Which of the following is the best interpretation of x in this context?
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The graph shows the relationship between the number of shares of stock from Company A, x, and the number of shares of stock from Company B, y, that Simone can purchase. Which equation could represent this relationship?
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For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k?
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For a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which function m models the number of minutes it will take Juan to ride x miles at this rate?
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s = 40 + 3t The equation gives the speed s, in miles per hour, of a certain car t seconds after it began to accelerate. What is the speed, in miles per hour, of the car 5 seconds after it began to accelerate?
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The function f is defined by f(x) = 1 ⁄ 10 x − 2. What is the y-intercept of the graph of y = f(x) in the xy-plane?
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5x + 7y = 1 ax + by = 1 In the given pair of equations, a and b are constants. The graph of this pair of equations in the xy-plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines?
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The equation x + y = 1,440 represents the number of minutes of daylight (between sunrise and sunset), x, and the number of minutes of non-daylight, y, on a particular day in Oak Park, Illinois. If this day has 670 minutes of daylight, how many minutes of non-daylight does it have?
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A store sells two different-sized containers of blueberries. The store’s sales of these blueberries totaled 896.86 dollars last month. The equation 4.51x + 6.07y = 896.86 represents this situation, where x is the number of smaller containers sold and y is the number of larger containers sold. According to the equation, what is the price, in dollars, of each smaller container?
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Kaylani used fabric measuring 5 yards in length to make each suit for a men’s choir. The relationship between the number of suits that Kaylani made, x, and the total length of fabric that she purchased, y, in yards, is represented by the equation y − 5x = 6. What is the best interpretation of 6 in this context?
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Argon is placed inside a container with a constant volume. The graph shows the estimated pressure y, in pounds per square inch (psi), of the argon when its temperature is x kelvins. What is the estimated pressure of the argon, in psi, when the temperature is 600 kelvins?
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The function f is defined by f(x) = 4x − 3. What is the value of f(10) ?
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A veterinarian recommends that each day a certain rabbit should eat 25 calories per pound of the rabbit’s weight, plus an additional 11 calories. Which equation represents this situation, where c is the total number of calories the veterinarian recommends the rabbit should eat each day if the rabbit’s weight is x pounds?
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Line r in the xy-plane has a slope of 4 and passes through the point (0, 6). Which equation defines line r ?
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What is the slope of the graph of y = 1 ⁄ 3 (29x + 10) + 5x in the xy-plane?
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Each term in the sequence below is nine less than the previous term. What is the ninth term of the sequence?
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Each term in the sequence below is 3 ⁄ 2 more than the previous term. What is the eighth term of the sequence?
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Each term in the sequence below is seven less than the previous term. What is the value of x – y?
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Each term in the sequence below is six more than the previous term. What is the value of x + z?
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Each term in the sequence below is 1 ⁄ 3 more than the previous term. What is the value of a + b + c + d?
Medium