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Elena wanted to find the slope and the y-intercept of the graph of 25 x - 20 y = 100. She decided to put the equation in slope-intercept form first. Here is her work:
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Anonymous
0

25x -20 y = 100


20y = 100 + 25x


y = 5 + \frac{5}{4}x


She concluded that the slope is \frac{5}{4} and the y-intercept is (0,5).


  1. What was Elena’s mistake?
  2. What are the slope and y -intercept of the line? Explain or show your reasoning.


Sangeetha Pulapaka
1
  1. Elena's first mistake was not changing the sign of the constant term when shifting it to the opposite side. The equation 25 x - 20 y = 100, when solved for y would be 25x - 100 = 20 y or y = -5 + \frac{5}{4}x.
  2. The equation, y = \frac{5}{4}x -5 is in the slope intercept form y = mx + b where m is the slope and b is the y-intercept. So, the slope is \frac{5}{4} and the y-intercept is -5.