Examine the two distinct lines defined by the following two equations in slope-intercept form.
line ℓ: y=34x+6
line k: y=34x−7
Are lines ℓ and k parallel? Justify your response.
1.Yes, lines ℓ and k are parallel because their slopes are equal.
2.No, lines ℓ and k are not parallel because their slopes are not equal.
3.No, lines ℓ and k are not parallel because their slopes are proportional.
4.Yes, lines ℓ and k are parallel because their slopes are proportional.
m = 34 for both. Same slope, m, means parallel
the answer is A, for anyone who might be confused
Examine the two distinct lines defined by the following two equations in slope-intercept form.
line ℓ: y=34x+6
line k: y=34x−7
Are lines ℓ and k parallel? Justify your response.
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Well, let me put on my clown shoes and juggle some slope-intercept form equations for you!
The equations of the two lines are:
Line ℓ: y = 34x + 6
Line k: y = 34x - 7
To determine if two lines are parallel, we need to check if their slopes are equal. So, let's take a look at the slopes of lines ℓ and k. Both equations have the same coefficient (34) in front of the x term.
Now, when it comes to parallel lines, their slopes need to be equal, not just proportional. So, if the slopes are the same, these lines will be running alongside each other like two synchronized dancers. If not, they'll be heading in different directions, like two clowns trying to find the circus tent.
Comparing the slopes of lines ℓ and k, we see that they are both equal to 34. Therefore, the correct answer is:
1. Yes, lines ℓ and k are parallel because their slopes are equal.
Now, go ahead and celebrate like a clown who just pulled off a triple somersault!
The correct answer is option 1: Yes, lines ℓ and k are parallel because their slopes are equal.
To determine if two lines are parallel, we need to compare their slopes. In slope-intercept form, the equation of a line is y = mx + b, where m is the slope of the line.
In this case, line ℓ has a slope of 34 and line k also has a slope of 34. Since the slopes are equal, we can conclude that the lines ℓ and k are parallel.
To get the slope, we can directly observe the coefficient of x in the equation. So, the slope of line ℓ is 34, and the slope of line k is also 34. As the slopes are equal, the lines ℓ and k are parallel.