2 – Vocabulary of a Line (No Calculator) Inequality Investigations 2 – Vocabulary of a Line (No Calculator)

Vocabulary Review Equation of a Line Slope-Intercept Form Point-Slope Form m – slope b – value of vertical intercept m – slope – point on the line Vertical Line Horizontal Line Slope – undefined Slope - 0

More Vocabulary Review Slope – rate of change…. Positive Slope - Increasing Negative Slope - Decreasing Vertical intercept (y) – the value at which a graph crosses the vertical axis Horizontal intercept (x) – the value at which a graph crosses the horizontal axis

Geometric Transformations Given the graph of f(x) and a positive constant a: f(x + a) moves the graph left a units f(x – a) moves the graph right a units f(x) + a moves the graph up a units f(x) – a moves the graph down a units – f(x) reflects line over x-axis

The value of the horizontal intercept is –2. 1. Given the graph of the line to the right: the value of the x-intercept is p the value of the slope is n Find the value of p + n. The slope is 4 6 The value of the horizontal intercept is –2.

The value of the vertical intercept is 5. 2. Given the graph of the line to the right: the value of the y-intercept is r the value of the slope is q Find the value of r + q. The slope is –3 4 The value of the vertical intercept is 5.

3. A line is graphed in the xy-plane to the right 3. A line is graphed in the xy-plane to the right. Which of the following is an equation of the line? –3 2

4. A line is graphed in the xy-plane to the right 4. A line is graphed in the xy-plane to the right. Which of the following is an equation of the line? y = 3.5

X X X 5. Which of the following is the graph of the equation A. B. Slope Positive Increasing X X C. D. y-intercept –2

Slope Positive – Increasing y-intercept - Positive 6. The equation y = ax + b is graphed in the xy-plane. If a and b are positive constants, which of the following could be the graph of y = –ax – b in the xy-plane. A. B. y = ax + b a > 0, b > 0 Slope Positive – Increasing y-intercept - Positive y = –ax – b –a < 0, –b < 0 Slope Negative – Decreasing y-intercept – Negative C. D.

7. The equation 6 – 2y = x is graphed in the xy-plane 7. The equation 6 – 2y = x is graphed in the xy-plane. Which of the following is a true statement about the graph? The graph’s x-intercept is 6 and its y-intercept is –2. The graph’s x-intercept is 6 and its y-intercept is 2. The graph has a slope of –2. D. The graph has a slope of

8. Which of the following is an equation of the line in the xy-plane with 7y – 28x = 8 B. 7y + 28x = 8 C. –7y + 28x = 8 D. –7y – 28x = 8

Parallel line – same slope 9. Which of the following is an equation of the line in the xy-plane that passes through the point (1, 1) and is parallel to the line with equation y = –3x – 1? X m = –3 Parallel line – same slope X X

10. Which of the following is an equation of the line in the xy-plane that passes

11. During a major snowstorm, snow fell at the rate of approximately 1 11. During a major snowstorm, snow fell at the rate of approximately 1.8 inches per hour for 5 hours. A. How much snow fell after one hour? one hour – 1.8 inches B. How much snow fell after two hours? two hours – 3.6 inches C. How much snow fell after three hours? three hours – 5.4 inches

11. During a major snowstorm, snow fell at the rate of approximately 1 11. During a major snowstorm, snow fell at the rate of approximately 1.8 inches per hour for 5 hours. Which of the following graphs represents the relationship between total snowfall during the storm, s, in inches and time, t, in hours? X A. B. Alternative Solution (2, 3.6) 0 inches of snow had fallen at t = 0 (0, 0) Only Graph A passes through (0, 0) (1, 3.5) (1, 1.8) X X C. D. (1, 8) (2, 1.8) (1, 1.8)

12. Anatoli is keeping track of the salt supply at his restaurant 12. Anatoli is keeping track of the salt supply at his restaurant. As of May 1st, the restaurant has a supply of 7.5 kilograms of salt. He estimates that the salt supply will decrease linearly and become empty in 20 weeks. Let w represent the number of weeks after May 1st. Let s represent the restaurant’s supply of salt in kilograms. Find two ordered pairs (w, s) which would be on a graph of salt supply.

12. Anatoli is keeping track of the salt supply at his restaurant 12. Anatoli is keeping track of the salt supply at his restaurant. As of May 1st, the restaurant has a supply of 7.5 kilograms of salt. He estimates that the salt supply will decrease linearly and become empty in 20 weeks. Let w represent the number of weeks after May 1st. Let s represent the restaurant’s supply of salt in kilograms. Find two ordered pairs (w, s) which would be on a graph of salt supply. (0, 7.5)

12. Anatoli is keeping track of the salt supply at his restaurant 12. Anatoli is keeping track of the salt supply at his restaurant. As of May 1st, the restaurant has a supply of 7.5 kilograms of salt. He estimates that the salt supply will decrease linearly and become empty in 20 weeks. Let w represent the number of weeks after May 1st. Let s represent the restaurant’s supply of salt in kilograms. Find two ordered pairs (w, s) which would be on a graph of salt supply. (0, 7.5) (20, 0)

12. Anatoli is keeping track of the salt supply at his restaurant 12. Anatoli is keeping track of the salt supply at his restaurant. As of May 1st, the restaurant has a supply of 7.5 kilograms of salt. He estimates that the salt supply will decrease linearly and become empty in 20 weeks. Which of the following graphs respresents s, the restaurant’s supply of salt in kilograms, as a function of w, the number of weeks after May 1st, if Anatoli is correct? A. X B. Alternative Solution Only Graph A passes through (20, 0) (0, 7.5) (20, 7.5) (0, 0) (20, 0) (0, 7.5) X X C. D. (0, 20) (20, ??) (0, 0) (20, ??)

13. The width of a rectangle is 4 more than half the length 13. The width of a rectangle is 4 more than half the length. If l represents length and w represents width, which of the following graphs represents the relationship between l and w? X A. B. X X C. D.

14. The line graphed in the xy-plane can be written as the equation y = m(x – 2) + 4, where m is a constant. Which of the following represents the graph of y = mx? A. B. C. D.

X 14. The line graphed in the xy-plane can be written as the equation y = m(x – 2) + 4, where m is a constant. Which of the following represents the graph of y = mx? X A.

14. The line graphed in the xy-plane can be written as the equation y = m(x – 2) + 4, where m is a constant. Which of the following represents the graph of y = mx? B.

X 14. The line graphed in the xy-plane can be written as the equation y = m(x – 2) + 4, where m is a constant. Which of the following represents the graph of y = mx? X C.

14. The line graphed in the xy-plane can be written as the equation y = m(x – 2) + 4, where m is a constant. Which of the following represents the graph of y = mx? D.

X 14. The line graphed in the xy-plane can be written as the equation y = m(x – 2) + 4, where m is a constant. Which of the following represents the graph of y = mx? B. X D.

15. The line graphed in the xy-plane can be written as the equation y = m(x – 3) + 2, where m is a constant. Which of the following represents the graph of y = m(x – 2) – 2? A. B. C. D.

15. The line graphed in the xy-plane can be written as the equation y = m(x – 3) + 2, where m is a constant. Which of the following represents the graph of y = m(x – 2) – 2? f(x – 2) to f(x – 3) moves 1 right f(x) – 2 to f(x) + 2 moves 4 up Choose a point, move 1 right and 4 up

15. The line graphed in the xy-plane can be written as the equation y = m(x – 3) + 2, where m is a constant. Which of the following represents the graph of y = m(x – 2) – 2? A. B. C. D.