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Question 153151This question is from textbook elementary and intermediate algebra concepts and applications
: I'm really having a hard time figuring these out can somebody help me please?
1. How do we write the equation of a horizontal line? What would be an example?
2. How do we write the equation of a vertical line? What would be an example?
3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M.
The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N.
a. Form the equations of both the lines. Show your work.
b. What are the co-ordinates of the point of intersection of lines M and N?
c. Write the co-ordinates of the intersections of lines M and N with the x-axis.
d. Write the co-ordinates of the intersection of lines M and N with the y-axis.
This question is from textbook elementary and intermediate algebra concepts and applications
Found 2 solutions by mangopeeler07, stanbon:
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! 1. How do we write the equation of a horizontal line? What would be an example?
The equation of a horizontal line does not have an x term. So therefore, y=mx+b becomes y=b. Set a value for b, such as y=3, and there you have it.
2. How do we write the equation of a vertical line? What would be an example?
This is just like a horizontal line, only there is no y value. So like y=b, you would just have x=b. once again, set a value for b, such as x=2, and there you have it.
3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M.
The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N.
a. Form the equations of both the lines. Show your work.
First get the slopes. slope equals the change in y over the change in x. So just grab any two coordinates of each line and plug in the y and x values. Let's use the easiest:
Line M: 3-5/9-13=-2/-4 or 1/2
So y=mx+b becomes y=1/2x+b
Plug in coordinates again,
3=1/2(9)+b
Solve
3=4.5+b
-1.5=b
~~~y=1/2x-3/2----------------Line M~~~
Line N: 3-5/-9--11=-2/2 or -1
y=-x+b
Plug in coordinates
3=-(-9)+b
3=9+b
Solve
-6=b
~~~y=-x-6--------------------------Line N~~~
b. What are the co-ordinates of the point of intersection of lines M and N?
You must solve the system of:
y=1/2x-3/2
y=-x-6
Set the values equal to each other
-x-6=1/2x-3/2
Solve
-1/2x-6=-3/2
-1/2x=9/2
x=9
Plug in x to get y.
y=-x-6
y=-9-6
y=-15
(9,-15)
c. Write the co-ordinates of the intersections of lines M and N with the x-axis.
(9,-15)--------------------------9 is x.
d. Write the co-ordinates of the intersection of lines M and N with the y-axis.
(9,-15)------------------------- -15 is y.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! 1. How do we write the equation of a horizontal line? What would be an example?
Ans: y = 3 is a horizontal line.
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2. How do we write the equation of a vertical line? What would be an example?
Ans: x = 3 is a vertical line.
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3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M.
The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N.
a. Form the equations of both the lines. Show your work.
Line M:
slope = (13-9)/(5-2) = 4/2 = 2
Intercept: 9 = 2*3+b
b = 3
Equation: y = 2x + 3
-------------------------
Line N:
slope = (-11--9)/(5-3) = -2/2 = -1
Intercept: -9 = -1*3 + b
b = -6
Equation: y = -x-6
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b. What are the co-ordinates of the point of intersection of lines M and N?
2x+3 = -x-6
3x = -9
x = -3
Substitute to solve for "y":
y = 2(-3)+3 = -3
Point of intersection (-3,-3)
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c. Write the co-ordinates of the intersections of lines M and N with the x-axis.
M Equation: y = 2x + 3
Let y = 0
0 = 2x + 3
x = -3/2
-----------------
N Equation:y = -x-6
Let y = 0
0 = -x-6
x = -6
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d. Write the co-ordinates of the intersection of lines M and N with the y-axis.
Let x = 0
M Equation: y = 2x + 3
y-intercept y = 3
-------------
N Equation: y = -x-6
y-intercept y = -6
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Cheers,
Stan H.
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