Question 39747: can you help me?
What is the equation of the line that passes through the points (-2,2) and (0,5) ?
Answer by Fermat(136)   (Show Source):
You can put this solution on YOUR website! If you have two points, (x1,y1) and (x2,y2) then the slope of the line joining them is given by,
m = (y1-y2) / (x1-x2)
We have (x1,y1) = (-2,2) and (x2,y2) = (0,5) so,
m = (2 - 5) / (-2 - 0) = -3/-2
m = 1.5
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The equation of any straight line can be written as,
y = mx + c
where m is the slope and c is the y-intercept.
The slope of the line joining (-2,2) and (0,5) is m = 1.5. So the eqn is,
y = 1.5x + c
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Any point on this line will satisfy the equation of the line. That means that we can put the x- and y-coordinates into the equation and we will get the lhs = the rhs.
The point (0,5) is one of the points we know lies on the line, so its x- and y-coordinates will satisfy the equation of the line if we we put x = 0 and y = 5 into the equation. This gives us,
5 = 0 + c
Since lhs = rhs, then
c = 5
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Finally,
y = 1.5x + 5
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