SOLUTION: 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

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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:
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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