SEARCH HOME
 Math Central Quandaries & Queries
 Question from Mark: What is y as an expression in terms of x?

Hi Mark,

When you commonly see this is where you have an equation involving $x$ and $y$ and perhaps involving other variables and you are asked to write $y$ as an expression in terms of $x.$ This means that you are to manipulate the equation you have to obtain an equivalent equation of the form

$y = \mbox{ an expression containing x but not y.}$

For example suppose the original equation is $x^2 + 3y - 7 - x - y = 0.$ First you only want terms containing $y$ on the left side of the equation so add $-x^2 +7 + x$ to each side to get

$x^2 + 3y - 7 - x - y -x^2 + 7 + x = -x^2 +7 + x$

which simplifies to

$3y - y = x^2 +7 + x \mbox{ or } 2y = x^2 + x + 7.$

Multiplying each side by $\large \frac12$ yields

$y = \frac12 \left(x^2 + x + 7\right)$

which is equivalent to the original equation $x^2 + 3y - 7 - x - y = 0$ but written as $y$ as an expression in terms of $x.$

I hope this helps,
Penny
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8732109069824219, "perplexity": 148.11390901715313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335491.4/warc/CC-MAIN-20220930145518-20220930175518-00411.warc.gz"}