SOLUTION: write an equation in slope intercept form of the line having the given slope and passing through the given point: m=-3,(4,-1)

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Question 197545: write an equation in slope intercept form of the line having the given slope and passing through the given point: m=-3,(4,-1)
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
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 (4, -1)

  • it has a slope of -3



First, let's draw a diagram of the coordinate system with point (4, -1) 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=-3, and system%28+x%5B1%5D+=+4%2C+y%5B1%5D+=+-1+%29+, we have the equation of the line:

y=-3%2Ax+%2B+11

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:




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