Slopes of parallel and perpendicular lines

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rachelmaddie

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Can you please check my work for this question?6CD701D1-9DD2-4FC4-A459-896C1D02CB83.png

Get both equations into the form y = mx + b. Then look at the slope
If the slopes are equal, the lines are parallel
If the slope of one is the negative reciprocal of the other(products are equal to -1), the lines are perpendicular
3x + 7y = 15
7x - 3y = 6
In the slope- intercept form m = slope, b = y intercept
y = 15 - 3x/7
y = 15/7 - 3/7x
The slope of the first line is -3/7
7x - 3y = 6
y = 7x - 6/3
y = 7/3x - 2
The slope of the second line is 7/3

Second step, Compare the slopes
Since -3/7 is not equal to 7/3, line 1 and line 2 are not parallel
To check for perpendicular lines m1 * m2 = (-3/7) * (7/3) = -1
Lines l1 and l2 are perpendicular because the product of their slopes is -1.
 
rachelmaddie said:
Can you please check my work for this question?View attachment 15477

Get both equations into the form y = mx + b. Then look at the slope
If the slopes are equal, the lines are parallel
If the slope of one is the negative reciprocal of the other(products are equal to -1), the lines are perpendicular
3x + 7y = 15
7x - 3y = 6
In the slope- intercept form m = slope, b = y intercept
y = 15 - 3x/7
y = 15/7 - 3/7x
The slope of the first line is -3/7
7x - 3y = 6
y = 7x - 6/3
y = 7/3x - 2
The slope of the second line is 7/3

Second step, Compare the slopes
Since -3/7 is not equal to 7/3, line 1 and line 2 are not parallel
To check for perpendicular lines m1 * m2 = (-3/7) * (7/3) = -1
Lines l1 and l2 are perpendicular because the product of their slopes is -1.
Click to expand...
Correct
 
rachelmaddie said:
Can you please check my work for this question?View attachment 15477

Get both equations into the form y = mx + b. / . . . /

3x + 7y = 15
7x - 3y = 6

In the slope- intercept form m = slope, b = y intercept

y = 15 - 3x/7\(\displaystyle / / / / / \) (1)
y = 15/7 - 3/7x
The slope of the first line is -3/7

7x - 3y = 6
y = 7x - 6/3 \(\displaystyle / / / / / \) (2)
y = 7/3x - 2
The slope of the second line is 7/3
Click to expand...

(1) This is incorrect. All terms are to be shown divided by 7.
The slope-intercept form is
y = (-3/7)x + 15/7.

(2) This is incorrect. All terms are to be shown divided by -3.
The slope-intercept form is
y = (7/3)x - 2.
 
lookagain said:
(1) This is incorrect. All terms are to be shown divided by 7.
The slope-intercept form is
y = (-3/7)x + 15/7.

(2) This is incorrect. All terms are to be shown divided by -3.
The slope-intercept form is
y = (7/3)x - 2.
Click to expand...
Are you saying to add that in the steps?
 
rachelmaddie said:
Are you saying to add that in the steps?
Click to expand...
Your answer is correct.

Your work is mostly correct. Addition of parentheses will remove all objections. You wrote:

3x + 7y = 15
7x - 3y = 6
In the slope- intercept form m = slope, b = y intercept
y = (15 - 3x)/7
y = 15/7 - 3/7x
The slope of the first line is -3/7
7x - 3y = 6
y = (7x - 6)/3 ......................... you skipped a step here. However, in my opinion that is insignificant.
y = 7/3x - 2
The slope of the second line is 7/3

Note those (). Those make subsequent statements true.
 
rachelmaddie said:
Are you saying to add that in the steps?
Click to expand...

The problem is that your conversion to y = mx + b form is sloppy. You can't divide by 7 in 2 steps, first 3x, then 15! When you write y = 15 - 3x/7 this is no longer the same equality. To keep it the same you need to divide all terms on both sides by 7. Also, 3x/7 is ambiguous. Please use parentheses: (3x)/7.
 
lev888 said:
The problem is that your conversion to y = mx + b form is sloppy. You can't divide by 7 in 2 steps, first 3x, then 15! When you write y = 15 - 3x/7 this is no longer the same equality. To keep it the same you need to divide all terms on both sides by 7. Also, 3x/7 is ambiguous. Please use parentheses: (3x)/7.
Click to expand...
Can you please show me?
 
Subhotosh Khan said:
Did you look at response #5?

You are NOT studying the responses before asking questions!!
Click to expand...
Get both equations into the form y = mx + b. Then look at the slope
If the slopes are equal, the lines are parallel
If the slope of one is the negative reciprocal of the other(products are equal to -1), the lines are perpendicular
3x + 7y = 15
7x - 3y = 6
In the slope- intercept form m = slope, b = y intercept
y = (-3/7)x + 15/7
y = 15/7 - 3/7x
The slope of the first line is -3/7
7x - 3y = 6
y = (7/3)x - 2
The slope of the second line is 7/3

Second step, Compare the slopes
Since -3/7 is not equal to 7/3, line 1 and line 2 are not parallel
To check for perpendicular lines m1 * m2 = (-3/7) * (7/3) = -1
Lines l1 and l2 are perpendicular because the product of their slopes is -1.
 
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