SOLUTION: Find the equation of the line that passes through (5,0) and has a slope of -2/3

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Question 748581: Find the equation of the line that passes through (5,0) and has a slope of -2/3
Found 2 solutions by MathLover1, Cromlix:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the line that passes through (5,0) and has a slope of -2%2F3=-0.67
Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (5, 0)

  • it has a slope of -0.67



First, let's draw a diagram of the coordinate system with point (5, 0) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=-0.67, and system%28+x%5B1%5D+=+5%2C+y%5B1%5D+=+0+%29+, we have the equation of the line:

y=-0.67%2Ax+%2B+3.35

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph:



Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Using y- b = m(x - a)
with m = -2/3
and (5, 0)
y - 0 = -2/3(x - 5)
y = -2/3x + 10/3
or
3y = -2x + 10