Question 127448: This is from a worksheet.
Write the equation of the line that passes through point (1,-8) with a slope of 0.
A) x=-8
B) y=1
C) y=-8
D) x=1
If the slope is zero, I came up with x=-8. Is that correct?
Found 2 solutions by MathLover1, Earlsdon:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
that is correct
C) 
| Solved by pluggable solver: FIND a line by slope and one point |
What we know about the line whose equation we are trying to find out:
- it goes through point (1, -8)
- it has a slope of 0
First, let's draw a diagram of the coordinate system with point (1, -8) plotted with a little blue dot:
Write this down: the formula for the equation, given point  and intercept a, is
 (see a paragraph below explaining why this formula is correct)
Given that a=0, and  , we have the equation of the line:
Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point ( ,  ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out:  . So, then, the equation of the line is:  .
Here's the graph:
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Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! Remember that a line having a zero slope is a horizontal line!
If such a line passes through the point (1, -8), then its equation is y = -8.
Why? Because a horizontal line (m = 0) passing through the point (1, -8) is the locus of all points whose y-coordinate is -8, and it doesn't matter what the x-coordinate is.
If the equation of your line were x = -8, you would have a vertical and the slope of a vertical line is undefined.
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