SOLUTION: What is the value of k so that the line (2+k)x + (2-k)y = 15 has a slope of 3/2?

Algebra ->  Linear-equations -> SOLUTION: What is the value of k so that the line (2+k)x + (2-k)y = 15 has a slope of 3/2?      Log On


   

Question 206009: What is the value of k so that the line (2+k)x + (2-k)y = 15 has a slope of 3/2?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The goal here is to first get the standard equation Ax%2BBy=C into the slope-intercept equation y=mx%2Bb


%282%2Bk%29x+%2B+%282-k%29y+=+15 Start with the given equation.


%282-k%29y+=+15-%282%2Bk%29x Subtract %282%2Bk%29x from both sides.


%282-k%29y+=+-%282%2Bk%29x%2B15 Rearrange the terms.


y+=+%28-%282%2Bk%29x%2B15%29%2F%282-k%29 Divide both sides by 2-k to isolate "y".


y+=+-%28%282%2Bk%29%2F%282-k%29%29x%2B15%2F%282-k%29 Break up the fraction


Now the equation is in the form y=mx%2Bb where the slope is m=-%282%2Bk%29%2F%282-k%29 and the y-intercept is b=15%2F%282-k%29


Because we want the slope to be 3%2F2, this means that m=3%2F2


So the next step is to solve 3%2F2=-%282%2Bk%29%2F%282-k%29 for 'k'. I'll let you do that.