# 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.

03:56

### 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.