SOLUTION: Consider the lines y = 3x + 7 and x + 2y = -10 Are the lines parallel? Explain why by comparing the slopes of the lines. Are the lines perpendicular? Explain why by co

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Question 387629: Consider the lines y = 3x + 7 and x + 2y = -10
Are the lines parallel? Explain why by comparing the slopes of the lines.

Are the lines perpendicular? Explain why by comparing the slopes of the lines.

Do the lines intersect? Explain why.

Found 2 solutions by rfer, gwendolyn:
Answer by rfer(16322) (Show Source):
You can put this solution on YOUR website!
y=3x+7
2y=-x-10
y=-1/2x-5
1st part
no
2nd part
no
3rd part
yes at (-3,-3.5)
I will let you do the explanations

Answer by gwendolyn(128) (Show Source):
You can put this solution on YOUR website!
Let's put both line equations into slope-intercept form:
y = mx + b, where m is the slope of the line.

The first equation is already in the right form:
y = 3x + 7, so it has a slope of 3.
The second equation is:
x + 2y = -10, subtracting x from both sides:
x + 2y - x = -10 - x
2y = -10 - x or
2y = -x - 10
And dividing each side by 2 to isolate y:
, distributing the division:
, or
y = - (1/2)*x - 5
so the slope of the second line is -1/2
So the answer to the first question is that the lines are not parallel, since the slopes are not identical.
Lines are perpendicular if the slopes are negative reciprocals of each other. The negative reciprocal of the first slope (3) is , but the slope of the second line is , so the answer to the second question is that the lines are not perpendicular.
The last question is whether the lines intersect. Since the lines are not parallel (see question 1), they must intersect somewhere (the question doesn't ask us to find where).