MTH 103 Group Activity Problems (W2B) Name: Equations of Lines Section 2.1 part 1 (Due April 13) platform. height 5 ft

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1 MTH 103 Group Activity Problems (W2B) Name: Equations of Lines Section 2.1 part 1 (Due April 13) Learning Objectives Write the point-slope and slope-intercept forms of linear equations Write equations for horizontal, vertical, parallel and perpendicular lines Model data with lines and linear functions Observe the following wheelchair ramp: ramp 13 ft platform height 5 ft base of ramp 12 ft Write complete answers, with verbal explanations given and any necessary calculations shown, for each question. 1. a. Notice that a ramp is a real-life application of a straight line. Write a description of how you can measure the steepness of a ramp. b. Does the ramp shown have the same steepness throughout or is the steepness changing? Explain your answer. c. Calculate the steepness of the ramp shown above. 3. a. Draw two different ramps that have different dimensions but have the same steepness. b. How do you know they have the same steepness? Include calculations and a verbal explanation. 1

2 c. Create 4 different ramps with the same steepness as a ramp with a height of 3 cm and base length of 12 cm. Each ramp should be a different size. Label the dimensions for each ramp you draw. Show calculations to prove the steepness is the same for each ramp. 4. Create a ramp with the same steepness as in #3(c), but with a base length of 1 cm. c. Explain how you could change the height of the original ramp if you increased its base length from 12 cm to 13 cm but wanted the new ramp to have the same steepness as the original in #4(a). If you know two points (x 1, y 1 ) and (x 2, y 2 ) that lie on a line, how do we compute the slope of the line? slope formula 2

3 Distance (miles) 5. Find the slope of the following line. Show what you did to compute the slope. Desmos.com Time (in minutes) 6. Carmen sets out on foot from home on her way to school. Suppose the graph above shows the distance (in miles) that Carmen has traveled from home at time t (in minutes). a. How fast is Carmen walking? Explain how you found her speed. b. If she arrives at school 1 hour after leaving home, how far is her school from her house? 3

4 Amount of water (oz) 7. A leaky faucet drips water into a measuring cup. The graph below shows the water level in the measuring cup over time. Amount of Water in Measuring Cup Time (in minutes) a) What does the point (0, 2) on the graph of the line tell you about the situation? Include values and units in your explanation. b) What does the point (10, 5) on the graph of the line tell you about the situation? Include values and units in your explanation. c) How fast is the water level in the measuring cup changing? Include values and units in your explanation. Explain how you get this information from the graph. d) Approximate how long it takes until there are 6 oz of water in the measuring cup. What coordinate on the graph did you look at to get this information? e) Approximate how many oz of water are in the cup after 5 minutes. What coordinate on the graph did you look at to get this information? 4

5 Any non-vertical line can be written in point-slope form and slope-intercept form. The general equations for these forms can be found on pages 69 and 70 of your textbook. point-slope form slope-intercept form 8. Find the equation of the line with slope 3 that goes through the point (1, 2) using point-slope form. 9. Find the equation of the line with slope 3 that goes through the point (1, 2) using slope-intercept form. 10. Suppose a babysitter charges her clients $54 to babysit 2 children for 4 hours. 6 of the 54 dollars are part of the babysitter s fixed transportation cost for travelling to her client s house. a. Find the equation of the line that goes through the points (0, 6) and (4, 54). b. What does the slope of this line mean in the context of the problem? Include units. c. What does the y-intercept of this line mean in the context of the problem? Include units. What is true about the slope of parallel lines? The slopes of parallel lines are equal Parallel and Perpendicular Lines What is true about the slope of perpendicular lines? The slopes of perpendicular lines are negative reciprocals of each other 5

6 11. Identify the following pairs of lines as parallel, perpendicular, or neither. Circle your answer. Remember: You need the equation of the line to be in slope-intercept form before you can compare the slopes. a. y = 3x + 1 and y = 4x + 1 parallel perpendicular neither b. y = 1 x 2 and y = 1 x + 1 parallel perpendicular neither 2 2 c. y = 6x + 2 and y = 6x 3 parallel perpendicular neither d. y 3 = 2(x + 3) and y 4 = 2(x 1) parallel perpendicular neither e. y + 2 = 6(x 3) and y 4 = 2(x 3) parallel perpendicular neither f. y = 10x + 50 and y = 10x 50 parallel perpendicular neither g. 2x 6y = 12 and 2x + y = 1 parallel perpendicular neither h. 1.5x + 3y = 0 and 3x 6y = 2 parallel perpendicular neither i. 4x y = 2 and 1 x + 2y = 1 parallel perpendicular neither Find the equation of the line parallel to f(x) = 2x + 6 that goes through the point (1,3). 13. Find the equation of the line perpendicular to f(x) = 2x + 6 that goes through the point (1,3). Graph the 3 lines from (12) and (13) on the grid below. Make sure to clearly label your axes. Graph paper from desmos.com 6

LINEAR EQUATIONS IN TWO VARIABLES

LINEAR EQUATIONS IN TWO VARIABLES What You Should Learn Use slope to graph linear equations in two " variables. Find the slope of a line given two points on the line. Write linear equations in two variables.