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Extra info for Quantitative Analysis
Although there will be two equations, the finalized graph will look as if there was only one line drawn. ) 7KHVHĆOLQHVĆLQWHUVHFWĆZLWKĆHDFKĆRWKHUĆ 7KHVHĆOLQHVĆDUHĆSDUDOOHOĆ 7KHVHĆOLQHVĆFRLQFLGHĆ GLDJUDP GLDJUDP GLDJUDP Here are the equations that produced the graphs above: 5x + 4y = 20 4x – 5y = 20 6x – 4y = 12 3x – 2y = 18 5x – 2y = 10 10x – 4y = 20 slope = –5/4 (0, y) = (0, 5) (x, 0) = (4, 0) slope = 4/5 (0, y) = (0, –4) (x, 0) = (5, 0) slope = 6/4 (0, y) = (0, 3) (x, 0) = (2, 0) slope = 3/2 (0, y) = (0, –9) (x, 0) = (6, 0) slope = 5/2 (0, y) = (0, –5) (x, 0) = (2, 0) slope = 10/4 (0, y) = (0, –5) (x, 0) = (2, 0) We can analyze what elements of the linear equations will produce each of the possible interactions.
Find the y-intercept for each given equation: 5x – 2y = 20 → b = C/B = 20/–2 = 10 → (0, –10) 10x – 4y = 20 → b = C/B = 20/–4 = –5 → (0, –5) 3. Use the information obtained to determine how the lines will interact with each other: The slopes are equal but the y-intercepts are not. Thus, the lines will be parallel to each other. 17b Determine whether these lines will be parallel, perpendicular, coincide, or just intersect: 5x + 4y = 9 y= 4 x+9 5 Follow these steps: 1. 8 2. 25) y = (4/5)x + 9 → b = 9 → (0, 9) 3.
14d Write a slope-intercept equation for the line that has the given slope and passes through the given point: slope = 0, P = (1, 2) Since we know the slope, we know that m = 0…and, since we know a point through which the graphed line will pass, we know (x, y) and that x1 = 1 when y1 = 2. 14e Write a slope-intercept equation for the line that has the given slope and passes through the given point: slope = undefined, P = (–3, –1) When the slope of the line is undefined, we cannot really use the point-slope formula to determine the desired equation.