How do you determine whether lines are parallel, perpendicular or neither? The equations given are y=1/3x +1/2 and y=1/3x-2. Once again please show me how you came to your answer. I do not just want the answer I need to see how you came to your answer, maybe you guys will show me something the book doesn't.
2006-12-16 14:19:28 · 7 answers · asked by 2good4hem 3 in Science & Mathematics ➔ Mathematics
The slope is the number in front of the x when the equation is written in the form y = mx + b. Since both your equations are written in this form, you can see that they both have 1/3 in front of the x and so they both have a slope of 1/3. Parallel lines are lines which have the same slope but different y interecepts. The y intercept is the number that stands alone, the b, which is 1/2 for your first equation and -2 for your second equation. So these equations are parallel.
For perpendicular lines, look at the slope of the given line, flip it over, change the sign, and use that for the slope of a perpendicular line. So if you wanted a line perpendicular to these lines, take the 1/3 and flip it over, get 3. Then change the sign and get -3. So the perpendicular line would be any line in the same plane that has a slope of -3.
Try graphing these lines and you'll see.
2006-12-16 14:27:23 · answer #1 · answered by Joni DaNerd 6 · 1⤊ 1⤋
To determine whether the 2 lines are parallel or perpendicular, you have to:
- Find the gradient
The gradient (m) is the coefficient of x when the equation is in the form of y = mx + c . The 2 equations are in this form.
For y = 1/3x + 1/2 ,
gradient, m1 = 1/3
For y = 1/3x - 2
gradient, m2 = 1/3
- If 2 lines are parallel, gradients are equal: m1 should be equal to m2
If 2 lines are perpendicular, product of gradients ( m1 * m2) = -1
Since m1 = m2 and m1 * m2 = 1/9
The 2 lines are parallel (symbol : //)
2006-12-16 14:43:32 · answer #2 · answered by GB 1 · 0⤊ 0⤋
The lines are parallel because when they appear in slope-intercept form y=mx+b the m= the slope. Since the the y-intercept is b=1/2 and b= -2 they are diiferent lines.
To be perpendicular the lines in slope-intercept form will be oppsite reciporcals ex (3/2x) and (-2/3x). even if the slopes are reciporcals but not opposite signs they are not perpendicular
they are neither if they intersect or are the same line.
ex y=2x+6 and y=4/7x+2 they are same if the equation in this form matches completey
2006-12-16 14:35:22 · answer #3 · answered by Jdicu812 1 · 0⤊ 0⤋
Two lines are parallel if they have the same slope.
They are perpendicular if the slope of one is the negative reciprocal of the other. For example, if one line has a slope of 2/3 and the other line has a slope of -3/2, the lines are perpendicular.
The slope is the number in front of the x when the equation is in slope-intercept form (which both if your equations are: y = mx + b).
2006-12-16 14:22:06 · answer #4 · answered by Jim Burnell 6 · 1⤊ 1⤋
Parallel lines have the same slope, m, the coefficient of 'x'.
Lines are perpendicular, if the product of the slopes equals -1.
Your equations are in slope-intercept form, so, there you are.
2006-12-16 14:25:19 · answer #5 · answered by S. B. 6 · 0⤊ 0⤋
Well, lines are parallel if their slopes are the same and their y-intercepts are different, so your lines in your question are parallel. If two lines have slopes that are negative reciprocals (i.e., when you multiply the two slopes together, you get -1), then they are perpendicular.
Steve
2006-12-16 14:22:18 · answer #6 · answered by Anonymous · 0⤊ 0⤋
12x + 4y = 16 4y = 16 - 12x y = -3x + 4 slope m1 = -3 (y = mx + c) 5y - 22 = -15x y = -3x + 22/5 slope m2 = -3 thus, both lines are parallel to each other since they have same slope
2016-05-23 01:09:21 · answer #7 · answered by Anonymous · 0⤊ 0⤋