Chapter 7 Linear Equations in Two Variables
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1 Chapter 7 Linear Equations in Two Variables. Graph the ordered pairs (, ), (, ), (, ), and (0, ). Graph the ordered pairs (, ), (, ), (, 0), and (, ).. Is (, ) a solution of y x 5? Is (, ) a solution of y x?.. Is (, ) a solution of x?. Is (, ) a solution of y x?.. 9. Is (0, 0) a solution of y x? 0. Is (, ) a solution of y x? Find the ordered pair solution of y x corresponding to x = Find the ordered pair solution of y x corresponding to x =.. 5. Find the ordered pair solution of y x corresponding to x =. 6. Find the ordered pair solution of x 6 corresponding to x =
2 Solve.. A physics student measured the speed of impact of a solid ball dropped from various heights above the ground and recorded the results as the following ordered pairs: (, 6), (, ), (, 7), (, ). The first component of the ordered pair is the height in feet, and the second component is the distance in feet the ball bounced. Graph the ordered pairs. The speed of a steel ball as it rolls down a ramp is recorded as the following ordered pairs: (0, 0), (, ), (, 6), (, 9). The first component of an ordered pair is the time in seconds, and the second component is the speed in feet per second. Graph the ordered pairs. Solve.. Given f ( x) 5x, find f (6). Given f ( x) 6x 7, find f ( ).. 5. Given g( x) x x, find g( ). 6. Given st () t, find s ( )
3 Find the x- and y-intercepts and graph.. y x 5 y x. x. y x 5. x 6. x
4 7. y x 6 8. y x. x y x y 6. x y 6. x y 6
5 5. x y x 8. x y. x y 6. x y 5. x 6. x
6 Solve.. The equation for the speed of a ball that is thrown straight up with an initial speed of 0 ft/s is v 0 t, where v is the speed of the ball after t seconds. Graph the equation for 0 t. The point whose coordinates are (, 98) is on the graph. Write a sentence that describes this ordered pair. Loren is a mathematics tutor. The equation that describes her wages is w = 0t, where t is the number of hours she spends tutoring, and w is her wages in dollars. Graph this equation for 0 t 0. The point whose coordinates are (6, 60) is on the graph. Write a sentence that describes this ordered pair. 6. The equation that describes the total number of feet traveled by a roller coaster in t seconds at its maximum speed is given by D 99t, where D is in feet. Graph this equation for 0 t 0. The point whose coordinates are (6, 59) is on this graph. Write a sentence that describes this ordered pair.. The equation that describes the cost of manufacturing n snow boards is C 75n 500, where C is the cost in dollars. Graph this equation for 0 n 00. The point whose coordinates are (60, 9000) is on the graph. Write a sentence that describes this ordered pair.
7 Find the slope of the line containing the points. Slope=run/rise.. P(, ), P (, ) P(, ), P (, 5). 7. P P (, ), (, ). P(, ), P(, ).. 5. P(0, ), P(, ) 6. P(, ), P(, ) Graph by using the slope and y-intercept. Convert the equation to standard form first: y=ax+b.. y x x y. x y. x y 6
8 8 Solve. Show work.. Find the equation of the line which contains the point (0, ) and has slope. Find the equation of the line which contains the point (, 0) and has slope... Find the equation of the line which contains the point (, ) and has slope. Find the equation of the line which contains the point (, ) and has slope.. 5. Find the equation of the line which contains the point (, ) and has 6. Find the equation of the line which contains the point (, ) and has 5. slope. slope. 6.. Find the equation of the line which passes through the points (, ) and (, ). Find the equation of the line which passes through the points (, ) and (, 8)..
9 Solve.. A runner in the 6.-mile Chicago Marathon was timed at several mileage points. The line of best fit is y 8x, where x is the time in hours, and y is the distance in miles. Time, x (hours) Distance, y (miles) 8 6 Graph the data and the line of best fit in the coordinate system below. Write a sentence that describes the meaning of the slope of the line of best fit in the context of this problem.. 9 Campers driving up a mountain use a Global Positioning System (GPS) to track their elevation. The base of the mountain is not at sea level. The line of best fit is y 50.x 06.7, where x is the time driving in minutes and y is the height above sea level in feet. Time, x (min) Height, y (ft) Graph the data and the line of best fit in the coordinate system below. Write a sentence that describes the meaning of the slope of the line of best fit in the context of this problem.
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1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled