The line 𝐴𝐵 is parallel to the
𝑥-axis. If the coordinates of the points 𝐴
and 𝐵 are seven, negative two and negative seven, 𝑘, respectively, find the value
Any line that is parallel to the
𝑥-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 𝑥-coordinates, and
dividing those two answers.
In this case, we know that the
value of 𝑚 or the gradient is zero. Substituting in the two coordinates
in this case gives us an equation zero equals negative two minus 𝑘 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 𝑘. And finally adding 𝑘 to both sides
of the equation gives us our answer 𝑘 equals negative two.
You’ll hopefully noticed that the
value of 𝑘 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 𝑥-axis will have the same 𝑦-coordinates.
In the diagram, we can see that the
horizontal line parallel to the 𝑥-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