Question

Kim has a lawn service business. The equation 165 - 105x + 3y = 0 relates y, her weekly profits, and x, the number of lawns she tends in a week. Kim incorrectly thinks that the slope of the mine represented by the equation is -105. Why did Kin think -105 was the slope?

Answer 1

Kim might have thought -105 was the slope by misinterpreting the coefficient of x in the equation 165 - 105x + 3y = 0. The accurate slope is found by dividing the coefficient of x by the coefficient of y, which results in a slope of 35, not -105.

Step-by-step explanation:

Kim might have incorrectly thought that the slope of the line represented by the equation 165 - 105x + 3y = 0 was -105 because she misinterpreted the coefficient of the variable x as the slope.

However, in the standard form ax + by = c, which in her case would be -105x + 3y = -165 after rearrangement, the slope m of the line is actually the negative coefficient of x divided by the coefficient of y, which is m = 105 / 3.

Therefore, the correct slope is 35, not -105. The slope indicates the change in y (weekly profits) for every one unit change in x (the number of lawns she tends in a week).