Soru
A. The lines have the same slopes and the same y- intercepts B. The lines have the same slopes but different y- intercepts. C. The lines have different slopes and different ý intercepts. D. The lines have different slopes and the same y- intercepts Four different systems are described on the left.Which describes the graph for each system? System A square System B Systemic c System D
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4.7
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Usta · 5 yıl öğretmeni
Uzman doğrulaması
Cevap
To determine which option describes the graph for need to analyze the given information about the lines in each system.Step 1: Analyze System A- The equation of the line in System A is given as y = 2x + 3.- This equation is in the form of y = mx + b, where m represents the slope and b represents the y-intercept.- From the equation, we can see that the slope (m) is 2 and the y-intercept (b) is 3.Step 2: Analyze System B- The equation of the line in System B is given as y = 2x - 1.- Again, this equation is in the form of y = mx + b.- From the equation, we can see that the slope (m) is 2 and the y-intercept (b) is -1.Step 3: Analyze System C- The equation of the line in System C is given as y = -3x + 2.- This equation is also in the form of y = mx + b.- From the equation, we can see that the slope (m) is -3 and the y-intercept (b) is 2.Step 4: Analyze System D- The equation of the line in System D is given as - 2.- Once again, this equation is in the form of y = mx + b.- From the equation, we can see that the slope (m) is -3 and the y-intercept (b) is -2.Now, let's match the descriptions with the systems:A. The lines have the same slopes and the same y-intercepts.- This description does not match any of the systems since none of them have the same slopes and y-intercepts.B. The lines have the same slopes but different y-intercepts.- This description matches System A and System B, as both have the same slope (m = 2) but different y-intercepts (b = 3 for System A and b1 B).C. The lines have different slopes and different y-intercepts.- This description matches System C and System D, as both have different slopes (m = -3 for System C and m = -3 for System D) and different y-intercepts (b = 2 for System C and b = -2 for System D).D. The lines have different slopes and the same y-intercepts.- This description does not match any of the systems since none of them have different slopes and the same y-intercepts.Therefore, the correct answer is:C. The lines have different slopes and different y-intercepts.