Sample Solutions

Step 1. Pick 3 values to substitute into 𝑥 in the given equation and solve for 𝑦. This will create 3 points to plot Step 2. Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work. Step 3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of line. #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 1) 𝑥 + 𝑦 = 7 1a) (0,7) (1,6) (2,5) 1b) and 1c) Step 1. Pick 3 values to substitute into 𝑥 in the given equation and solve for 𝑦. This will create 3 points to plot Step 2. Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work. Step 3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of line. #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 3) 𝑥 + 2𝑦 = 12 3a) (0,12) (6,3) (12,0) 3b) and 3c) #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 5) 3𝑥 − 2𝑦 = 6 5a) (2,0) (0, −3) (4,3) 5b) and 5c) #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 7) 4𝑥 + 𝑦 = 24 7a) (6,0) (0,24) (3,12) 7c) and 7d) #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 9) 𝑦 = 3𝑥 − 4 9a) (0, −4) (1, −1) (2,2) 9b) and 9c) #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 11) 𝑦 = −6𝑥 + 5 11a) (0,5)(1, −1)(2, −7) 11b) and 11c) #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 1 13) 𝑦 = 𝑥 − 2 2 13a) (0, −2) (2, −1)(4,0) 13b) and 13c) #1 – 15: a) Find three points b) plot the points c) Sketch a graph. 1 15) 𝑦 = − 𝑥 + 7 3 15a) (0,7)(3,6)(6,5) 15b) and 15c) Step 1. Find the x- and y-intercepts of the line. Let 𝑦 = 0 and solve for x to find the 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡. Let 𝑥 = 0 and solve for y to find the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡. Step 2. Find a third solution to the equation by picking any number and plugging it in for x solve for y. Step 3. Plot the three points and check that they line up. Step 4. Draw the line #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 17) 𝑥 + 2𝑦 = 10 17a) (10,0) 17b) (0,5) 17c) (2,4) 17d) Step 1. Find the x- and y-intercepts of the line. Let 𝑦 = 0 and solve for x to find the 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡. Let 𝑥 = 0 and solve for y to find the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡. Step 2. Find a third solution to the equation by picking any number and plugging it in for x solve for y. Step 3. Plot the three points and check that they line up. Step 4. Draw the line #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 19) 3𝑥 − 2𝑦 = 24 19a) (8,0) 19b) (0,12) 19c) (2 − 9) 19d) Step 1. Find the x- and y-intercepts of the line. Let 𝑦 = 0 and solve for x to find the 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡. Let 𝑥 = 0 and solve for y to find the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡. Step 2. Find a third solution to the equation by picking any number and plugging it in for x solve for y. Step 3. Plot the three points and check that they line up. Step 4. Draw the line #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 21) 2𝑥 + 3𝑦 = 24 21a) (12,0) 21b) (0,8) 21c) (3,6) 21d) #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 23) 𝑦 = 3𝑥 − 6 23a) (2,0) 23b) (0, −6) 23c) (1, −3) 23d) #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 25) 𝑦 = 2𝑥 + 8 25a) (−4,0) 25b) (0,8) 25c) (1,10) 25d) #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 1 27) 𝑦 = 𝑥 − 4 2 27a) (8,0) 27b) (0, −4) 27c) (2 − 3) 27d) #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 1 29) 𝑦 = − 𝑥 + 15 3 29a) (45,0) 29b) (0,15) 29c) (15,10) 29d) #17 - 32: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 1 31) 𝑦 = 𝑥 + 10 2 31a) (−20,0) 31b) (2,11) 31c) (0,10) 31d) #33 – 42 a) Find three points b) Plot the points c) Sketch a graph. d) Use the graph to find the x-intercept (say there is no x-intercept if the graph does not cross the x-axis). e) Use the graph to find the y-intercept (say there is no y-intercept if the graph does not cross the y-axis.) 33) 𝑥 = 2 33a) (2,0) (2,4) (2,6) 33d) (2,0) 33e) None 33b) and 33c) 33 – 42 a) Find three points b) Plot the points c) Sketch a graph. d) Use the graph to find the x-intercept (say there is no x-intercept if the graph does not cross the x-axis). e) Use the graph to find the y-intercept (say there is no y-intercept if the graph does not cross the y-axis.) 35) 𝑦 = 5 35a) (0,5) (3,5) (6,5) 35d) None 35e) (0,5) 35b) and 35c) 33 – 42 a) Find three points b) Plot the points c) Sketch a graph. d) Use the graph to find the x-intercept (say there is no x-intercept if the graph does not cross the x-axis). e) Use the graph to find the y-intercept (say there is no y-intercept if the graph does not cross the y-axis.) 37) 𝑥 + 5 = 0 37a) (−5,0) (−5,4) (−5,6) 37d) (−5,0) 37e) None 37b) and 37c) 33 – 42 a) Find three points b) Plot the points c) Sketch a graph. d) Use the graph to find the x-intercept (say there is no x-intercept if the graph does not cross the x-axis). e) Use the graph to find the y-intercept (say there is no y-intercept if the graph does not cross the y-axis.) 39) 𝑦 − 3 = 9 39a) (0,6) (3,6) (6,6) 39d) None 39e) (0,6) 39b) and 39c) 33 – 42 a) Find three points b) Plot the points c) Sketch a graph. d) Use the graph to find the x-intercept (say there is no x-intercept if the graph does not cross the x-axis). e) Use the graph to find the y-intercept (say there is no y-intercept if the graph does not cross the y-axis.) 41) 3𝑥 = 21 41a) (7,0) (7,3) (7,6) 41d) (7,0) 41e) None 41b) and 41c) 43) The following graph depicts the sale of boxes of girl scout cookies. Interpret the meaning of the point (20, 100) $100 is earned from selling 20 boxes of cookies. OR 20 boxes of cookies cost $100. Or something like this. There are many correct answers. 45) The graph below shows the hourly temperature at different times during the afternoon. Interpret the meaning of the point (5,72.00) At 5 in the afternoon the temperature is 72 degrees.