### Video Transcript

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.

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

Letโs 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 ๐ฆ two minus ๐ฆ one over ๐ฅ two minus ๐ฅ one. 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. ๐ฆ two equals ๐ minus ๐ฆ one, which is eight, over ๐ฅ two, which is negative six, minus ๐ฅ one, which is one.

Now, thereโs 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 thatโs negative seven. Now we need to work on isolating ๐. To do that, Iโll 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 weโre 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, letโs try to solve by graphing. Okay, hereโs a sketch of our graph. Letโs start by graphing the point that we were given: one, eight. Hereโs where point one, eight would fall. Now, what do we know about this line? We know that itโs parallel to the ๐ฅ-axis, which means we know what it will look like. Itโs a horizontal line.

Now, letโs try to graph our second point: negative six, ๐. We know that the ๐ฅ-value will be negative six. We also know that this point must fall on our line. That means the only ๐ฆ-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.