Which of the following equations represents a line parallel to the 𝑥-axis? Is it A) negative nine 𝑦 minus seven equals zero, B) negative two 𝑥 minus 𝑦 equals zero, C) negative 𝑥 minus five 𝑦 equals three, or D) eight 𝑥 plus three 𝑦 equals negative nine?
The 𝑥-axis is horizontal. Any line that is parallel to this must also be horizontal. All of these lines will have equation 𝑦 equals 𝑐, where 𝑐 is a constant that can be found where the line intercepts the 𝑦-axis.
Options B, C, and D all contain an 𝑥 term. Therefore, none of those equations can be parallel to the 𝑥-axis. Option A, on the other hand, only contains a 𝑦 term and a constant. This can be rewritten in the form 𝑦 equals 𝑐. Adding nine 𝑦 to both sides of the equation gives us negative seven is equal to nine 𝑦. And, finally, dividing both sides of this equation by nine gives us 𝑦 is equal to negative seven-ninths. Equation A will be parallel to the 𝑥-axis and will intercept the 𝑦-axis at negative seven-ninths.