Question 650306: Hi, I am able to answer the first part of the question, but am confused with how to describe the line in terms of it's relationship to the x and y axes. Please can you help me understand? Thank you.
Write the equation of the line that passes through (-4,5) with slope equal to zero.
y-5=0(x-(-4))
y-5=0
y=5
Describe this line in terms of its relationship to the x and y axes.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You correctly solved the first part of the problem. Your answer tells you that this equation:
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y - 5 = 0(x - (-4))
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will always be true if y = +5 because when you substitute +5 for y this equation becomes:
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0 = 0(x - (-4))
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which reduces to:
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0 = 0
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Notice that it does not matter what value you assign to x. x could be -100, +50, or any other value you choose. As long as y is +5, the slope of the graph of this equation will be zero.
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How does this translate to a graph? Any time that you are told that a line has a slope of zero, you can immediately say that it's graph is a horizontal line because its value of y never changes as you move to the right along the x-axis.
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In this problem, you calculated that the unchanging value of y is +5. Therefore, you can describe the graph as being horizontal (parallel to the x-axis) and crossing the y-axis at +5. In picture form:
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The horizontal red line above the x-axis is the graph of a line having a zero slope and a y value of +5. Note that on the x-axis at the point where x equals -4, the corresponding value of y as shown by the graph is +5, so the two original constraints (a zero slope graph having the x,y point (-4,5) on the line) are both satisfied.
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Hope this helps.
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