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# Analytic Geometry

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Hello my name is heily grade 10 student, my teacher gave us a problems which we haven't yet tackle, the instruction is to solve the problem in any way possible to test our resourcefulness dealing with new maths

Im trying to figure out how to answer but i dont find any reference to the internet how to answer in  "x + ___ y - ___=0"  way.

1.Find the equation of the line which contains the point (-2,3) and is parallel to the line 3x+5y=17. (write the numerical coefficient of each term to complete the required equation)
Answer would be: ___x + ___ y - ___ = 0

2.Find the equation of the lines that are both passing through the point (10,-8) with slopes 5 and -1/5.
Answer: ___ x - y - ____ = 0  (  my answer y=5x-58)
x + ___ y+ ____ = 0   (my answer y=-y=-1/5x-6)

3.Find the equations for two lines that both go through the point (1,2), one with slope 3 and one with slope -1/3. (write the numerical coefficient of each term to complete the required equation)
a. With the slope =3: __ x-y- ____=0  (my answer y=3x-1)
b. With slope = -1/3: x + ___ y - ___=0 (my answer y=-1/3x+7/3)

Jul 26, 2018
edited by Guest  Jul 26, 2018
edited by Guest  Jul 26, 2018

#1
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1.Find the equation of the line which contains the point (-2,3) and is parallel to the line 3x+5y=17. (write the numerical coefficient of each term to complete the required equation)
Answer would be: ___x + ___ y - ___ = 0

Let us find the slope of the given line...in the form Ax + By  = C, the slope will be given by   -A/B

So...the slope of the given line  =  -3/5

And since parallel lines have the same slope, we can  write an equation of a line having a slope of -3/5 and passing through ( -2,3) thusly

y  =(-3/5)(x -  -2)  + 3      simplify

y = (-3/5) ( x + 2)  + 3      multiply through by 5

5y  = -3(x + 2) + 15

5y = -3x - 6 + 15

5y = -3x + 9     add 3x to  both sides, subtract 9 from both sides

3x + 5y - 9 = 0

Jul 26, 2018
#2
+102320
+1

2.Find the equation of the lines that are both passing through the point (10,-8) with slopes 5 and -1/5.
Answer: ___ x - y - ____ = 0  (  my answer y=5x-58)
x + ___ y+ ____ = 0   (my answer y=-y=-1/5x-6)

First line

y = 5(x - 10) +  -8

y = 5x - 50 - 8

y = 5x - 58       subtract y from both sides

5x - y - 58  = 0     [  this is the same as your answer, just in "standard form" ]

Second line

y  = (-1/5) ( x - 10) + -8       multiply through by 5

5y  = (-1)(x - 10)  +  - 40  simplify

5y  = -x + 10  - 40

5y  = -x - 30      add x, 30 to both sides

x + 5y  + 30  = 0  [ your answer is in slope-intercept form and is correct.....I think they want "standard form" ]

Jul 26, 2018
#3
+102320
+1

3.Find the equations for two lines that both go through the point (1,2), one with slope 3 and one with slope -1/3. (write the numerical coefficient of each term to complete the required equation)
a. With the slope =3: __ x-y- ____=0  (my answer y=3x-1)
b. With slope = -1/3: x + ___ y - ___=0 (my answer y=-1/3x+7/3)

First line

y = (3)(x - 1) + 2

y = 3x - 3 + 2

y = 3x  -  1      subtract y from both sides and rearrange as

3x - y - 1  = 0   [ your answewr is correct in slope-intercept form ]

Second line

y= (-1/3) ( x - 1) + 2     multiply through by 3

3y = (-1)(x - 1) + 6

3y  = -x + 1 + 6

3y  = -x + 7       add x to both sides, subtract 7 from both sides

x + 3y  - 7   = 0

Jul 26, 2018
edited by CPhill  Jul 26, 2018