Video: Finding Slopes of Straight Lines

𝐴𝐡 is parallel to the 𝑦-axis. If the coordinates of the points 𝐴 and 𝐡 are (π‘š, 2) and (8, 6), respectively, find the value of π‘š.

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Video Transcript

The line 𝐴𝐡 is parallel to the 𝑦-axis. If the coordinates of the points 𝐴 and 𝐡 are π‘š, two and eight, six, respectively, find the value of π‘š.

If two straight lines are parallel, then their slopes or gradients are equal. As 𝐴𝐡 is parallel to the 𝑦-axis, then the slope of 𝐴𝐡 will be the same as the slope of the 𝑦-axis. The 𝑦-axis is a vertical line. This means that the slope is undefined. Therefore, line 𝐴𝐡 will also have a slope that is undefined.

The slope or gradient of any line is calculated using the formula 𝑦 two minus 𝑦 one divided by π‘₯ two minus π‘₯ one. Substituting in the coordinates of 𝐴 and 𝐡 β€” π‘š, two and eight, six β€” gives us that the slope is equal to six minus two divided by eight minus π‘š. However, as the slope of 𝐴𝐡 is undefined, the denominator in this case eight minus π‘š must be equal to zero.

Therefore, to work out the value of π‘š, we need to solve the equation eight minus π‘š equals zero. Adding π‘š to both sides of this equation gives us our solution π‘š equals eight. This means that the coordinates of 𝐴 are eight, two.

We could actually go a step further and say that any point on the line 𝐴𝐡 will have an π‘₯-coordinate of eight. This is because the equation of the vertical line that passes through eight, two and eight, six is π‘₯ equals eight.

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