SOLUTION: a line has slope negative 3 over 2 and passes through (5,3) which of these points is also on the line? (-4,9) (7,6) (2,6) (9,9)

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Question 117528: a line has slope negative 3 over 2 and passes through (5,3) which of these points is also on the line?
(-4,9) (7,6)
(2,6) (9,9)
Found 2 solutions by solver91311, edjones:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Since you are given the slope and a point that is not the y-intercept, you need to use the point-slope form of a line to define the equation.

y-y%5B1%5D=m%28x-x%5B1%5D%29
y-3=%28-3%2F2%29%28x-5%29

You can simplify this to:
2y-6=-3x%2B15
3x%2B2y=21

Now you can substitute the x and y coordinates for the given set of points and see which ordered pairs make the statement true. I'll check one of them and you can do the rest.

(-4,9)
3%28-4%29%2B2%289%29=6%3C%3E21 so the statement given those coordinate values is false and you can say that (-4,9) does NOT lie on the line.

Hope this helps.

Answer by edjones(8007) 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 (5, 3)

  • it has a slope of -1.5



First, let's draw a diagram of the coordinate system with point (5, 3) 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=-1.5, and system%28+x%5B1%5D+=+5%2C+y%5B1%5D+=+3+%29+, we have the equation of the line:

y=-1.5%2Ax+%2B+10.5

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:



None of the points go through the line.
Perhaps you made an error copying the question.
.
Ed