Question 1165813: Which of the lines defined here has/have only one unique intercept?
A. X = 8
B. -8x - 7y = -7
C. 9y = 5
D. -3x - 3y = 0
Possible answers
A. A, C, and D
B. A, and C
C. B, and D
D. B
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! horizontal lines will have one intercept only, unless they are identical to the x-axis.
in that case, they will have an infinite number of intercepts, depending on how you define an intercept.
vertical lines will have one intercept only, unless they are identical to the y-axis.
in that case, they will have an infinite number of intercepts, depending on how you define an intercept.
lines that are not vertical or horizontal and that intercept with the origin (the point (0,0) on the graph) will lave one intercpt only.
the rest will have two intercepts.
selection A is a vertical line not on the y-axis, therefore will have one intercept only, namely the x-axis.
selection B is a line that is a horizontal line not on the x-axis, therefore will have one intercept only, namely the y-axis.
selection C is is not vertical nor horizontal but does go through the origin, so it will have one intercept only.
selection D is not vertical nor horizontal but does go through the origin, so it will have one intercept only.
a vertical line will be in the form of x = c, where c is a constant.
a horizontal line will be in the form of y = c, where c is a constant.
a line that goes through the origin will be in the form of y = mx, where m is the slope.
a line that is not vertical nor horizontal nor goes through the origin is a line in the form of y = mx + b, where m is the slope and b is a constant that is not equal to 0.
x = 8 is a vertical line.
-8x - 7y = -7 looks like a line that is not vertical nor horizontal nor has a constant of 0.
to test, convert the line to slope intercept form.
start with -8x -7y = -7
add 8x to both sides of the equation to get -7y = 8x - 7
divide both sides by -7 to get y = -8x/7 + 1
our assumption is confirmed and so this line will have two intercepts.
note that a straight line will have one intercept or two intercepts, no more.
9y = 5 becomes y = 5/9
this is horizontal and will have one intercept only.
-3x - 3ty = 0 is transformed to slope intercept form as shown bwlow.
add 3x to both sides of the equation to get:
-3y = 3x
divide both sides by 3 to get:
y = -x.
this line is in y = mx + b form where b = 0, making it in y = mx form.
it will go through the origin, therefore will have one intercept only.
your selections are:
A,C,D.
only B has two intercepts.
the graphs of these lines are shown below.
here's a bunch of references from purplemath that should help you to understand straight lines and their intercepts and their equations.
https://www.google.com/search?q=straight+lines+purplemath&rlz=1C1GCEA_enUS874US874&oq=straight+lines+purplemath&aqs=chrome..69i57.5183j1j7&sourceid=chrome&ie=UTF-8
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