WEBVTT
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Given that the straight line passing through the points one, eight and negative six, ๐ is parallel to the ๐ฅ-axis, find the value of ๐.
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Letโs solve this equation in two different ways.
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First, weโll solve algebraically and then weโll solve by graphing.
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Letโs highlight some important information first.
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The line weโre talking about is a straight line that is parallel to the ๐ฅ-axis; this tells us something about our line.
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Primarily, it tells us that our slope is zero.
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Lines that are parallel to the ๐ฅ-axis have ๐ฆ-values that do not change.
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The ๐ฆ-values stay the same, so theyโre not moving up or down and the slope is zero.
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Letโs look at how we would solve this problem with algebra using the function for a slope of a line.
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We find the slope of the line by solving ๐ฆ two minus ๐ฆ one over ๐ฅ two minus ๐ฅ one.
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We can use the two points weโre given and plug them into this formula: ๐ฅ one, ๐ฆ one would be one, eight; ๐ฅ two, ๐ฆ two would be negative six, ๐.
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๐ฆ two equals ๐ minus ๐ฆ one, which is eight, over ๐ฅ two, which is negative six, minus ๐ฅ one, which is one.
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Now, thereโs one other piece of information that we can include here.
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We already know what our slope will be.
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Our slope is zero.
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Now, we need to solve for ๐ to figure out what is the value of this ๐ point.
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Our first step was subtract one from negative six, and thatโs negative seven.
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Now we need to work on isolating ๐.
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To do that, Iโll multiply both sides of the equation by negative seven.
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Negative seven times one over negative seven equals one.
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That cancels out.
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Negative seven times zero equals zero, and weโre left with zero equals ๐ minus eight.
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We will add eight to both sides to isolate ๐.
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Zero plus eight equals eight.
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๐ equals eight.
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Now, letโs try to solve by graphing.
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Okay, hereโs a sketch of our graph.
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Letโs start by graphing the point that we were given: one, eight.
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Hereโs where point one, eight would fall.
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Now, what do we know about this line?
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We know that itโs parallel to the ๐ฅ-axis, which means we know what it will look like.
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Itโs a horizontal line.
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Now, letโs try to graph our second point: negative six, ๐.
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We know that the ๐ฅ-value will be negative six.
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We also know that this point must fall on our line.
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That means the only ๐ฆ-value โ the only value ๐ can be โ is equal to eight.
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Negative six, eight is the second point that we were looking for.
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Both of these processes produce a solution of ๐ equal to eight; both of these processes help us to see that our ๐ value is equal to eight.