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Question 214449: 1. find the slope of the line that passes through the points (-2,3) and (5,-8).
2. find the equation of the line that passes through the points (3,-2)and(4,-2).
3. Find the equation, in standard form, with all interger coefficients, of the line perpendicular to x+ 3y=6 and passing through (-3,5).
Found 2 solutions by natroa08, alanc:
Answer by natroa08(4)   (Show Source):
You can put this solution on YOUR website! 1. when you are given 2 coordinates you can find the slope by using this formula ➔ slope(m) = y2-y1/x2-x1
so you get -8-3/5+2 = -11/7 ←thats your slope
2. since both the Y's are the same it tells you that it is a horizontal line there is no slope so the equation is y=-2
3. first we put the equation to the y= format. so....x+3y=6 turns into 3y=-x+6
the next step is to get rid of the 3y (to get rid of the 3y you must divide everything else by 3.) which gives you y= -1/3x+3
but thats not your answer, they are asking to find a line that's perpendicular to this one. to find the perpendicular line you change the slope to its opposite/reciprocal. which in this case would be 3. now its wants the line to pass through (-3,5) we wil use this to find our b. (point slope formula is y= mx+b). The formula to find b is..... b = y1 - mx1 (y1 and x1 are the coordinates and m is your slope)
(remember the subtraction sign means the opposite of that number) ok so lets solve for b.
b= 5-3(-3) this equals 14. now we have the final answer y=3x+14
hope that wasn't too confusing!
Answer by alanc(27)  (Show Source):
You can put this solution on YOUR website! 1.) We want to find the slope of a line intersecting points (-2, 3) and (5,-8) use the definition of slope. SLOPE = (Y2 - Y1)/(X2 -X1) for points (X1, Y1) AND (X2, Y2). (note the significance of parentheses )
Here, SLOPE = (-8 - 3)/(5- (-2)) = -11/7
2.) An equation of a line through (3,-2), (4, -2) follows from previous solver: y=-2 because the line is horizontal.
3.) Standard form for a line is Ax + By = C for A and B not both zero.
first find the slope of x + 3y = 6, rearranging it to y = (-1/3)x + 2
Slope is (-1/3) for given line. The slope of a line perpendicular to this is 3, it is the negative reciprocal of (-1/3).
Next we have y - 5 = 3* (x - (-3))
y - 5 = 3x + 9
3x -y = -14
Answer: 3x -y = -14
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