Video Transcript
Given that the points 𝐴 12, 10 and 𝐵 𝑥, negative eight lie on a line that has a slope of one, determine the value of 𝑥.
In this question, we are told that two points 𝐴 and 𝐵 lie on a line that has a slope of one. We want to use this to determine the missing coordinate in point 𝐵. To answer this question, let’s start by recalling what is meant by the slope of a line.
We recall that if we have a nonvertical line that passes through two distinct points with coordinates 𝑥 sub one, 𝑦 sub one and 𝑥 sub two, 𝑦 sub two, then its slope 𝑚 is given by 𝑦 sub one minus 𝑦 sub two all over 𝑥 sub one minus 𝑥 sub two. We are told in the question that the slope of the line is one. So, we can set 𝑚 equal to one. We can also set 𝑥 sub one and 𝑦 sub one equal to the coordinates of 𝐴 and 𝑥 sub two, 𝑦 sub two equal to the coordinates of 𝐵.
Substituting these values into the slope formula gives us one is equal to 10 minus negative eight all over 12 minus 𝑥. In the numerator, we can calculate that 10 minus negative eight is 18, since subtracting a negative is the same as adding the positive value. So, we have that one is equal to 18 over 12 minus 𝑥. We can now multiply both sides of the equation by 12 minus 𝑥.
We can also note at this point that 𝑥 cannot be equal to 12, since the line is not vertical because its slope is one. This gives us that 12 minus 𝑥 is equal to 18. We can then solve this equation for 𝑥. We subtract 12 from both sides of the equation and then multiply through by negative one to get that 𝑥 must be equal to negative six.
