SOLUTION: Hi, I could really use some help with this problem: Find the equation of the line whose x-intercept is 2/3 and whose y-intercept 3/2. Thanks in advance, Lou

Algebra ->  Linear-equations -> SOLUTION: Hi, I could really use some help with this problem: Find the equation of the line whose x-intercept is 2/3 and whose y-intercept 3/2. Thanks in advance, Lou      Log On


   

Question 44900: Hi,
I could really use some help with this problem:

Find the equation of the line whose x-intercept is 2/3 and whose y-intercept 3/2.

Thanks in advance,
Lou
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
For any linear equation ax+%2B+by+=+c, we have that the X-intercept is found by setting y to 0, getting ax=c. From that, we conclude that we can say that x+=+c%2Fa. The Y-intercept is, equally, c%2Fb. We find the lcm of 2 and 3 (so we can equal them), that is 6. Therefore, c = 6.
We solve:
6%2Fa+=+2%2F3
a+=+9
6%2Fb+=+3%2F2
b+=+4
Checking:
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 9+x+%2B+4+y+=+6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-9%2F4.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/9 = 0.666666666666667.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/4 = 1.5.
  • Slope is -9/4 = -2.25.
  • Equation in slope-intercept form: y=-2.25*x+1.5.