math_crasher
Can someone pls tell me whether the graphs of the lines will be collinear, parallel, or intersecting?
y= 4x+1
y=4x-3
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jim_thompson5910
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What are the slopes of each line?
pitankar
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intersecting
math_crasher
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why?
jim_thompson5910
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no, the lines aren't intersecting
math_crasher
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I just need the explaination of the formula to tell whether or not it is parallel or intersecting and col linear
jim_thompson5910
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What are the slopes of each line?
math_crasher
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thats all it is given, theres a formula for solving but I don't know it.
jim_thompson5910
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Hint: the equation y = mx+b has the slope m
jim_thompson5910
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ex: y = 9x + 20 has the slope of 9
pitankar
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sorry the lines are not intersecting. Extremely sorry, I made a mistake. They have same slopes, so they should be parallel.
math_crasher
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I guess its four right? thats fine
jim_thompson5910
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4 is the slope, yes
jim_thompson5910
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since the slope is 4 for both of the lines, the lines are either parallel or collinear
jim_thompson5910
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the two lines are collinear if and only if the two y-intercepts are the same
jim_thompson5910
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otherwise, the two lines are parallel
math_crasher
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ah ok
pitankar
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one passes from y=-3 and other from y=1, so they are parallel(since slopes are same) but not co-linear.
math_crasher
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so if its the same its parallel and what happens if its collinear?
jim_thompson5910
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no, if the y-intercepts are the same, the lines are collinear
if the y-intercepts are different, the lines are parallel
both cases are true when the slopes are both equal
math_crasher
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oh ok i see, so it is collinear right?
jim_thompson5910
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what are the y-intercepts for both lines?
math_crasher
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i need help finding the y intercepts pls
jim_thompson5910
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y = mx+b
b is the y-intercept
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ex:
for y = 2x+11
11 is the y-intercept
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ex:
y = 14x-13 which is the same as y = 14x + (-13)
-13 is the y-intercept
math_crasher
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ah i see
math_crasher
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in this case the y intercepts are the same, which is 4x? And what do I do with the 1 and -3?
pitankar
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to find Y=intercept, put x=0 in each equation. simple. Any point on y-axis is represented as x=0 and y=Y
jim_thompson5910
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no, that's not the y-intercept
jim_thompson5910
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y = 4x + 1, y intercept is 1
jim_thompson5910
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look back up at my 2nd to last post
math_crasher
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oh right then the y intercepts aren't the same
jim_thompson5910
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so the lines are parallel
math_crasher
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ah ok what will happen if its intersecting?
jim_thompson5910
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if the slopes are different, then the lines will intersect
math_crasher
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what about collinear?
jim_thompson5910
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if the slopes are the same and the y-intercepts are the same, then the two lines are collinear
math_crasher
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ah coolio thanks