Video: Finding the Slopes of Straight Lines

𝐴𝐡 is parallel to the π‘₯-axis. If the coordinates of the points 𝐴 and 𝐡 are (7, βˆ’2) and (βˆ’7, π‘˜) respectively, find the value of π‘˜.

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Video Transcript

The line 𝐴𝐡 is parallel to the π‘₯-axis. If the coordinates of the points 𝐴 and 𝐡 are seven, negative two and negative seven, π‘˜, respectively, find the value of π‘˜.

Any line that is parallel to the π‘₯-axis is a horizontal line; this means that you’ll have a gradient of zero. The gradient of any line can be calculated by subtracting the 𝑦-coordinates, subtracting the π‘₯-coordinates, and dividing those two answers.

In this case, we know that the value of π‘š or the gradient is zero. Substituting in the two coordinates in this case gives us an equation zero equals negative two minus π‘˜ divided by seven minus negative seven. Simplifying the denominator of the fraction leaves us with 14; seven minus negative seven is plus 14, positive 14. Multiplying both sides of this equation by 14 leaves this with zero equals negative two minus π‘˜. And finally adding π‘˜ to both sides of the equation gives us our answer π‘˜ equals negative two.

You’ll hopefully noticed that the value of π‘˜ is equal to the 𝑦-coordinate of our other points: seven, negative two. This is because any points that lie on a line that is parallel to the π‘₯-axis will have the same 𝑦-coordinates.

In the diagram, we can see that the horizontal line parallel to the π‘₯-axis that passes through negative seven, negative two and also the point seven, negative two has equation 𝑦 equals negative two. This is because it crosses the 𝑦-axis at the point negative two. This means that all the ordered pairs or coordinates that lie on the line will have a 𝑦-coordinate of negative two.

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