SOLUTION: What's the equation of the given lines in standard form?? Help Been stuck for hours ). The line with m = 4 and intersecting 2x -4y = 8 at x = 6. 2.) The line through (2, -1)

Algebra ->  Graphs -> SOLUTION: What's the equation of the given lines in standard form?? Help Been stuck for hours ). The line with m = 4 and intersecting 2x -4y = 8 at x = 6. 2.) The line through (2, -1)       Log On


   

Question 466443: What's the equation of the given lines in standard form?? Help Been stuck for hours
). The line with m = 4 and intersecting 2x -4y = 8 at x = 6.
2.) The line through (2, -1) and parallel to x - 2y = 6.
3.) The line with m = 4 and the point (0, -9).
4.)The line with a slope of -1/3 and b of 6.
5.)The line including two points (6, 4) and (-5, 3).
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Standard form of equation of a line:
Ax + By = C
Slope-intercept form of equation of a line:
y = mx + b
Point slope form of equation of a line:
(y - y1) = m(x - x1)
1) *************************************************
m = 4
Now we need a point on the line, the point where the 2 lines intersect at x=6
To find y value, substitute in 6 for x and solve for y.
2%286%29+-+4y+=+8
12+-4y+=+8
Subtract 12 on both sides
-4y+=+-4
Divide by -4 on both sides
y+=+1
Thus the point is (6,1)
We have slope and a point, use point-slope form:
y-1+=+4%28x-6%29
Distribute
y-1+=+4x+-24
Subtract 4x on both sides
-4x+%2By+-1+=+-24
Add 1 on both sides
-4x+%2B+y+=+-23
This is the equation of the line in standard form
2)***********************************************************
Parallel lines have equal slopes
Convert line x - 2y = 6 to slope-intercept form:
x+-+2y+=+6
Subtract x on both sides
-2y+=+-x+%2B6
Divide by -2 on both sides
y+=+x%2F2+-+3
From y=mx +b we see that m=1%2F2
Point on the line is (2,-1)
We have slope and a point, use point-slope form:
y%2B1+=+%281%2F2%29%28x-2%29
Distribute
y%2B1+=+x%2F2+-+1
Subtract x/2 on both sides
-x%2F2+%2B+y+%2B1+=+-1
Subtract 1 on both sides
-x%2F2+%2B+y+=+-2
Cannot have fractions in standard form
Multiply equation by 2 to cancel denominators
-x+%2B+2y+=+-4
This is the equation of the line in standard form
3)*******************************************************
m = 4
point on the line is (0,-9)
We have slope and a point, use point-slope form:
y+%2B+9+=+4%28x+-+0%29
Distribute
y%2B9+=+4x
Subtract 4x on both sides
-4x+%2By+%2B9+=+0
Subtract 9 on both sides
-4x+%2B+y+=+-9
This is the equation of the line in standard form
4)**********************************************************
slope = m = -1/3
y_intercept = b = 6
We have slope and y_intercept, use slope-intercept form:
y=mx+b
y+=+-%28x%2F3%29+%2B+6
Add x/3 on both sides
%28x%2F3%29%2By+=+6
Cannot have fractions in standard form
Multiply equation by 3 to cancel out denominator
x+%2B+3y+=+18
This is the equation of the line in standard form
5) **********************************************************
Given 2 points (6,4) and (-5,3)
Find slope using slope formula:
m+=+%28y2+-+y1%29%2F%28x2-x1%29
m+=+%283-4%29%2F%28-5-6%29
m+=+%28-1%29%2F-11
Division of 2 negative numbers equals a positive
m+=+1%2F11
Pick one of our points, say (6,4)
We have slope and a point, use point-slope form:
y-4+=+%281%2F11%29%28x-6%29
Distribute
+y+-4+=+%28x%2F11%29+-+6%2F11
Subtract x/11 on both sides
-%28x%2F11%29+%2B+y+-4+=+-6%2F11
Add 4 on both sides
Notice we have to add fractions, find common denominator
4 = 44/11
-6/11 + 44/11 = 38/11
-%28x%2F11%29+%2B+y+=+38%2F11
Cannot have fractions in standard form
Multiply equation by 11 to cancel out denominator
-x+%2B+11y+=+38
This is the equation of the line in standard form
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