(GEOMETRY, HELP PLEASE) Write the equation of the line with a slope of 3/7 passing through the point (9 -2)

- anonymous

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- anonymous

Show me the slope form ....?

- ParthKohli

\[y - y_1 = m(x - x_1) \]Here,\[m = {3 \over 7} \\ y_1 = -2\\x_1 = 9\]

- anonymous

what is x?

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## More answers

- anonymous

I got y=3/7x-2

- anonymous

hi

- anonymous

hi

- anonymous

did you get it

- anonymous

\[y=mx+b, y=-2, x=9, m=3/7\]
Solve for b.

- ParthKohli

Leave \(x\) and \(y\) just like \(x\) and \(y\).

- anonymous

ok

- anonymous

I got y=3/7x-2

- anonymous

\[-2=\frac{3}{7}(9)+b, b=?\]
And you got b=-2?

- anonymous

9?

- anonymous

@CliffSedge

- anonymous

You can also use the equation Parth gave:
\[y−y_1=m(x−x_1) \rightarrow y−(-2)=\frac{3}{7}(x−(9))\]

- anonymous

Assuming you've studied algebra before, this should look familiar.

- anonymous

2x-9= -3/7

- anonymous

Ok, let's back way up then.
The point is (9, -2) which means that at a particular point on the line, x=9, and y=-2.
The slope is 3/7 which means from any point on the line, you can go up 3 units then to the right 7 units and find another point on the line.

- anonymous

An equation of the line will be such that you can take the x and y coordinates from any point on the line and put them into the equation and make it a true statement.
The slope is found by dividing the difference between the y coordinates of two points by the difference between the x coordinates of those two points (rise-over-run).

- anonymous

This time is got 3x-7y=41

- anonymous

##### 1 Attachment

- anonymous

quick question, what type of triangle is RST?

- anonymous

That looks better. You can test it by putting in the x and y coordinates from your point and seeing if it makes the statement true. i.e. 3(9)-7(-2)=?

- anonymous

41

- anonymous

Okay great! thank you

- anonymous

Good, then the equation is true.
For triangle RST, do you know how to measure the sides using the distance formula (i.e. the pythagorean theorem)? As a hint, notice the symmetry and how the sides RS and RT look to be the same length.

- anonymous

is it isoscles?

- anonymous

That would be a good guess. I'd probably still measure to make sure it wasn't equilateral.
Can you see how long segment ST is?

- anonymous

I cant tell

- anonymous

The coordinates of points S and T are given. S is at (-4,7) and T is at (4,7). They are both at the height y=7, so it is a straight horizontal like going from x=-4 to x=4. How far is that?

- anonymous

I got isoscles. I check

- anonymous

Ok, I just want to make sure you know how to handle these questions in general in case you see a similar problem, that isn't so easy to solve.

- anonymous

There are particular skills and knowledge that these questions are testing from you. It is important that you have these basic skills proficiently so that you can move on to more difficult problems.

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