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Video: Finding the y-Coordinate of a Point Lying on a Straight Line That Is Parallel to the x-Axis given Another Point's Coordinates

Kathryn Kingham

Given that the straight line passing through the points (1,8) and (-6,k) is parallel to the x-axis, find the value of k.


Video Transcript

Given that the straight line passing through the points one, eight and negative six, ๐‘˜ is parallel to the ๐‘ฅ-axis, find the value of ๐‘˜.

Letโ€™s solve this equation in two different ways. First, weโ€™ll solve algebraically and then weโ€™ll solve by graphing. Letโ€™s highlight some important information first. The line weโ€™re talking about is a straight line that is parallel to the ๐‘ฅ-axis; this tells us something about our line. Primarily, it tells us that our slope is zero. Lines that are parallel to the ๐‘ฅ-axis have ๐‘ฆ-values that do not change. The ๐‘ฆ-values stay the same, so theyโ€™re not moving up or down and the slope is zero.

Letโ€™s look at how we would solve this problem with algebra using the function for a slope of a line. We find the slope of the line by solving ๐‘ฆ two minus ๐‘ฆ one over ๐‘ฅ two minus ๐‘ฅ one. We can use the two points weโ€™re given and plug them into this formula: ๐‘ฅ one, ๐‘ฆ one would be one, eight; ๐‘ฅ two, ๐‘ฆ two would be negative six, ๐‘˜. ๐‘ฆ two equals ๐‘˜ minus ๐‘ฆ one, which is eight, over ๐‘ฅ two, which is negative six, minus ๐‘ฅ one, which is one.

Now, thereโ€™s one other piece of information that we can include here. We already know what our slope will be. Our slope is zero. Now, we need to solve for ๐‘˜ to figure out what is the value of this ๐‘˜ point. Our first step was subtract one from negative six, and thatโ€™s negative seven. Now we need to work on isolating ๐‘˜. To do that, Iโ€™ll multiply both sides of the equation by negative seven. Negative seven times one over negative seven equals one. That cancels out. Negative seven times zero equals zero, and weโ€™re left with zero equals ๐‘˜ minus eight. We will add eight to both sides to isolate ๐‘˜. Zero plus eight equals eight. ๐‘˜ equals eight.

Now, letโ€™s try to solve by graphing. Okay, hereโ€™s a sketch of our graph. Letโ€™s start by graphing the point that we were given: one, eight. Hereโ€™s where point one, eight would fall. Now, what do we know about this line? We know that itโ€™s parallel to the ๐‘ฅ-axis, which means we know what it will look like. Itโ€™s a horizontal line.

Now, letโ€™s try to graph our second point: negative six, ๐‘˜. We know that the ๐‘ฅ-value will be negative six. We also know that this point must fall on our line. That means the only ๐‘ฆ-value โ€” the only value ๐‘˜ can be โ€” is equal to eight. Negative six, eight is the second point that we were looking for. 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.