Expert: Scott A Wilson - 7/18/2010

Question
I have a question that has been kicking my butt. The quetsion is
b) The slope is -2/3 and has the x-intercept as the line 3x-4y=6.
How do I answer this question?

Answer
The equation of a line is y = mx + b where m is the slope and b is the y-intercept.
This means that m = -2/3, so the equation, so far, is y = -2x/3  + b.

It then states that the same x intercept (that's where y=0) as the line 3x-4y=6.
Putting y=0 into this equation gives 3x=6.  Dividing both sides by 3 gives x=2.

To solve for b, note that the x-intercepts are the same, so x=2 and y=0 into y = -2x/3 + b.
Since y is 0, b = 2x/3 for x = 2.  From here, put in x and b is found.

Take y = -2x/3 + b and put in the value of b, so now we have the equation of the line.