equation of a line
- Thread starter mkay
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pka
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The slope is \(\displaystyle -2\) so the answer is \(\displaystyle 2x+y=0\).
I suspect a bit of explanation of how one should arrive at the answer might be helpful.
The origin is the point with coordinates (0, 0).
You are told that the point (-1, 2) is on the graph.
standard form for a linear equation is often written as
Ax + By = C
The point (0, 0) is on the graph, so we can substitute 0 for x, and 0 for y:
A*0 + B*0 = C
0 + 0 = C
0 = C
So, for this particular line, C = 0, and we can "refine" our equation to be
Ax + By = 0
And since the point (-1, 2) is on the graph as well, we can substitute -1 for x and 2 for y:
A(-1) + B(2) = 0
-A + 2B = 0
or, 2B = A
I think you can use ANY values for A and B which satisfy this relationship....for example, if A=4, and 2B = A, then B = 2....and you could write your equation this way: 4x + 2y = 0
That's surely not the ONLY way to write the equation, of course. If you want a simpler form, divide both sides of MY equation by 2, and you'll get 2x + y = 0.
Now, there's another way to find the equation of the line.....you could start by finding the slope of the line that contains (0, 0) and (-1, 2): (2 - 0)/(-1 - 0) = 2/(-1), or -2
So the slope of this line is -2. And the y-intercept (where the line crosses the y-axis) is 0, since the line crosses the y-axis at (0, 0).
The "slope-intercept form" for the equation of a line is
y = mx + b
where "m" is the slope and "b" is the y-intercept. Since our line has a slope of -2, and a y-intercept of 0, we can substitute for m and b:
y = -2x + 0
y = -2x
And....if you put that into standard form, do you also get 2x + y = 0?