Question

Devon wants to write an equation for a line that passes through 2 of the data points he has collected. The points are (8, 5) and (–12, –9). He writes the equation 7x – 10y = 3. Is this a good model? Explain your reasoning.

Answer 1

For this case we have the following equation:
 $7x - 10y = 3$
 From here, we must substitute ordered pairs of the form:
 (x, y)
 If the ordered pair satisfies the equation, then it belongs to the line.
 We have then:

 For (8, 5):
 We substitute the following values:
 $x = 8 y = 5 7 (8) - 10 (5) = 3 56 - 50 = 3 6 = 3$
 We observe that the equation is not satisfied and therefore, this point does not belong to the line.
 Since one of the points does not belong to the line, then the equation is not a good model.

 Answer:
 It is not a good model. One of the points does not belong to the line.