Video: Determining an Equation That Represents a Line Parallel to the π‘₯-Axis

Which of the following equations represents a line parallel to the π‘₯-axis? [A] βˆ’9𝑦 βˆ’ 7 = 0 [B] βˆ’2π‘₯ βˆ’ 𝑦 = 0 [C] βˆ’π‘₯ βˆ’ 5𝑦 = 3 [D] 8π‘₯ + 3𝑦 = βˆ’9.

01:39

Video Transcript

Which of the following equations represents a line parallel to the π‘₯-axis? Is it A) negative nine 𝑦 minus seven equals zero, B) negative two π‘₯ minus 𝑦 equals zero, C) negative π‘₯ minus five 𝑦 equals three, or D) eight π‘₯ plus three 𝑦 equals negative nine?

The π‘₯-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 π‘₯ term. Therefore, none of those equations can be parallel to the π‘₯-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 π‘₯-axis and will intercept the 𝑦-axis at negative seven-ninths.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.