Question 1071591: write an equation in standard form for a line passing through the pair of points. (-8,0) and (0,3).
Found 2 solutions by math_helper, Alan3354:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
Standard form is Ax + By = C where A,B,and C are constants (often integers).
Point-slope form is y = mx + b, where m=slope and b=y-intercept (i.e. value at x=0).
I've always found it easiest to work in point-slope form, then rearrange it to standard form at the end. Given the two points, the slope can be found as rise/run (change in y value over change in x):
[ It does not matter which point you use as start/end, but once you decide which point to use as the "end", be sure to use the companion y value as the ending y value ]
m = (y2-y1)/(x2-x1)
m = (3-0)/(0-(-8)) = 3/8
[ If we used the points the other way —> m = (0-3)/(-8-0) = -3/-8 = 3/8 ]
So far we have:
y = (3/8)x + b
To find 'b', choose one of the points, say (-8,0), then plug in and solve for b:
0 = (3/8)(-8) + b —> 0 = -3 + b —> b=3
Now we have
y = (3/8)x + 3
Re arranging to standard form:
-(3/8)x + y = 3
Technically, the above is acceptable. Some teachers may want you to make the coefficients integers if possible, and some *think* the coefficient in front of x should be positive (my Calculus book does not say this is a requirement). So here are other forms that are equally valid:
Multiply through by 8:
-3x + 8y = 24 (probably what most teachers expect)
Multiply through by -1:
3x - 8y = -24 (some teachers may want to see it expressed like this, A>0)
Good luck!
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! write an equation in standard form for a line passing through the pair of points. (-8,0) and (0,3).
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| x y 1|
|-8 0 1| = 0
| 0 3 1|
x*(0-3) - y*(-8 - 0) + 1*(-24-0) = 0
-3x + 8y = 24
or,
3x - 8y + 24 = 0
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