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

To determine which option describes the graph for need to analyze the given information about the lines in each system.<br /><br />Step 1: Analyze System A<br />- The equation of the line in System A is given as y = 2x + 3.<br />- This equation is in the form of y = mx + b, where m represents the slope and b represents the y-intercept.<br />- From the equation, we can see that the slope (m) is 2 and the y-intercept (b) is 3.<br /><br />Step 2: Analyze System B<br />- The equation of the line in System B is given as y = 2x - 1.<br />- Again, this equation is in the form of y = mx + b.<br />- From the equation, we can see that the slope (m) is 2 and the y-intercept (b) is -1.<br /><br />Step 3: Analyze System C<br />- The equation of the line in System C is given as y = -3x + 2.<br />- This equation is also in the form of y = mx + b.<br />- From the equation, we can see that the slope (m) is -3 and the y-intercept (b) is 2.<br /><br />Step 4: Analyze System D<br />- The equation of the line in System D is given as - 2.<br />- Once again, this equation is in the form of y = mx + b.<br />- From the equation, we can see that the slope (m) is -3 and the y-intercept (b) is -2.<br /><br />Now, let's match the descriptions with the systems:<br /><br />A. The lines have the same slopes and the same y-intercepts.<br />- This description does not match any of the systems since none of them have the same slopes and y-intercepts.<br /><br />B. The lines have the same slopes but different y-intercepts.<br />- 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).<br /><br />C. The lines have different slopes and different y-intercepts.<br />- 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).<br /><br />D. The lines have different slopes and the same y-intercepts.<br />- This description does not match any of the systems since none of them have different slopes and the same y-intercepts.<br /><br />Therefore, the correct answer is:<br />C. The lines have different slopes and different y-intercepts.