SOLUTION: graph each linear equation by finding and plotting it's intercepts (1) x-y=6 (2) x-y=-4 (3) x-y=4 (4) y=-4x (5) y=-5x (6) y=5x (7)x=5y (8)y=3x+6 (9)

Algebra ->  Functions -> SOLUTION: graph each linear equation by finding and plotting it's intercepts (1) x-y=6 (2) x-y=-4 (3) x-y=4 (4) y=-4x (5) y=-5x (6) y=5x (7)x=5y (8)y=3x+6 (9)       Log On


   

Question 37678: graph each linear equation by finding and plotting it's intercepts

(1) x-y=6
(2) x-y=-4
(3) x-y=4
(4) y=-4x
(5) y=-5x
(6) y=5x
(7)x=5y
(8)y=3x+6
(9) 2x=4
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
(1) x-y=6
-y=-x+6
y=x-6 with y-intercept at -6
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+-1+y+=+6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F-1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/1 = 6.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/-1 = -6.
  • Slope is -1/-1 = 1.
  • Equation in slope-intercept form: y=1*x+-6.
graph%28+500%2C+500%2C+6-8%2C+6%2B8%2C+-6-8%2C+-6%2B8%2C+1%2Ax%2B-6+%29+

(2) x-y=-4
-y=-x-4
y=x+4 with y-intercept at 4
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+-1+y+=+-4 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F-1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -4/1 = -4.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -4/-1 = 4.
  • Slope is -1/-1 = 1.
  • Equation in slope-intercept form: y=1*x+4.
graph%28+500%2C+500%2C+-4-8%2C+-4%2B8%2C+4-8%2C+4%2B8%2C+1%2Ax%2B4+%29+

(3) x-y=4
-y=-x+4
y=x-4 with y-intercept at -4
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+-1+y+=+4 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F-1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 4/1 = 4.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/-1 = -4.
  • Slope is -1/-1 = 1.
  • Equation in slope-intercept form: y=1*x+-4.
graph%28+500%2C+500%2C+4-8%2C+4%2B8%2C+-4-8%2C+-4%2B8%2C+1%2Ax%2B-4+%29+

(4) y=-4x with y-intercept at 0
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 4+x+%2B+1+y+=+0 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-4%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 0/4 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/1 = 0.
  • Slope is -4/1 = -4.
  • Equation in slope-intercept form: y=-4*x+0.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+-4%2Ax%2B0+%29+

(5) y=-5x with t-intercept at 0
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 5+x+%2B+1+y+=+0 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-5%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 0/5 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/1 = 0.
  • Slope is -5/1 = -5.
  • Equation in slope-intercept form: y=-5*x+0.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+-5%2Ax%2B0+%29+

(6) y=5x with y-intercept at 0
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -5+x+%2B+1+y+=+0 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--5%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 0/-5 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/1 = 0.
  • Slope is --5/1 = 5.
  • Equation in slope-intercept form: y=5*x+0.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+5%2Ax%2B0+%29+

(7) x=5y
y = (x/5) with y-intercept at 0
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+-5+y+=+0 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F-5.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 0/1 = 0.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 0/-5 = 0.
  • Slope is -1/-5 = 0.2.
  • Equation in slope-intercept form: y=0.2*x+0.
graph%28+500%2C+500%2C+0-8%2C+0%2B8%2C+0-8%2C+0%2B8%2C+0.2%2Ax%2B0+%29+

(8) y=3x+6 with y-intercept at 6
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -3+x+%2B+1+y+=+6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--3%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/-3 = -2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/1 = 6.
  • Slope is --3/1 = 3.
  • Equation in slope-intercept form: y=3*x+6.
graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+6-8%2C+6%2B8%2C+3%2Ax%2B6+%29+

(9) 2x=4
x = 2 where the x-intercept is 2 and there is no y-intercept
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
this equation defines a vertical line.

  • X intercept: 2. X intercept is the intersection of the line with the x axis.

  • Y intercept: not defined (the line IS vertical)

  • Slope: not defined, can be thought of as infinite

graph%28+500%2C+500%2C+2-5%2C+2%2B5%2C+-10%2C+10%2C+1000000x-1000000%2A2+%29+