they are making a bridge to be built over railroad track . the bridge will be perpendicular to the tracks and the middle of the bridges will be directly above the tracks. if the town is represented on a coordinate grid, the tracks are a straight line running through( 9,15) and (-12,-6) with one end of the bridge at (-8,8). the line perpendicular in point (-3,3)
write an equation of the line containing the railroad tracks in standard form ???
write an equation of the line containing the bridge in standard form ???
what is the other end of the bridge???
STEP BY STEP PLEASE
i keep getting different answer =( i will REALLY APPRECIATED if you help me
write an equation of the line containing the railroad tracks in standard form ???
write an equation of the line containing the bridge in standard form ???
what is the other end of the bridge???
STEP BY STEP PLEASE
i keep getting different answer =( i will REALLY APPRECIATED if you help me
-
Before I answer, just let me remind you that Slope = rise/run or y2-y1/x2-x1
With that being said, to find the equation of the line containing the railroad tracks you must find the slope of the line using two points on the railroad tracks ( 9,15) and (-12,-6)
-6-15/-12-9 = -21/-21 or 1. With that being said the slope of the line that the railroad tracks is on is 1, and because we know the bridge is perpendicular, the slope of the bridge must be -1. (negative recipricol)
Now, to find the next part of the equation we need, or the y-intercept, we will use the formular y = mx + b.
Basically, we will plug in the slope and a point on the line of the railroad tracks, I will use (9,15)
15 = 9(1) + b.<-------------let b represent the y intercept.
15 = 9 + b
-9 -9
6 = b
Now we know the equation of the tracks is y = 1(x) + 6.
The same thing is to be done for the bridge, using the point (-8,8)
8 = -8(-1) + b
8 = 8 + b
-8 -8
b = 0
Hence the equation of the line that the bridge is on is y = -1(x) + 0
To find the other end of the bridge, we must use relativity from the point (0,0).
Since we now know the middle of the bridge is (0,0), and one end is (-8,8), to find the unknown end we just move in the exact opposite way as (-8,8) which means up 8 and left 8. Since we are moving the opposite way from 0 we must go the opposite of up 8 and left 8 which is down 8 and right 8, leaving us at the point (8,-8), and that is the coordinate of the other end of the bridge!
So in summary of order of your questions
1. y = x + 6.
2. y = -x
3. (8,-8)
Hope I helped!
With that being said, to find the equation of the line containing the railroad tracks you must find the slope of the line using two points on the railroad tracks ( 9,15) and (-12,-6)
-6-15/-12-9 = -21/-21 or 1. With that being said the slope of the line that the railroad tracks is on is 1, and because we know the bridge is perpendicular, the slope of the bridge must be -1. (negative recipricol)
Now, to find the next part of the equation we need, or the y-intercept, we will use the formular y = mx + b.
Basically, we will plug in the slope and a point on the line of the railroad tracks, I will use (9,15)
15 = 9(1) + b.<-------------let b represent the y intercept.
15 = 9 + b
-9 -9
6 = b
Now we know the equation of the tracks is y = 1(x) + 6.
The same thing is to be done for the bridge, using the point (-8,8)
8 = -8(-1) + b
8 = 8 + b
-8 -8
b = 0
Hence the equation of the line that the bridge is on is y = -1(x) + 0
To find the other end of the bridge, we must use relativity from the point (0,0).
Since we now know the middle of the bridge is (0,0), and one end is (-8,8), to find the unknown end we just move in the exact opposite way as (-8,8) which means up 8 and left 8. Since we are moving the opposite way from 0 we must go the opposite of up 8 and left 8 which is down 8 and right 8, leaving us at the point (8,-8), and that is the coordinate of the other end of the bridge!
So in summary of order of your questions
1. y = x + 6.
2. y = -x
3. (8,-8)
Hope I helped!