{"id":1004,"date":"2022-02-03T05:33:13","date_gmt":"2022-02-03T05:33:13","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=1004"},"modified":"2022-02-03T05:33:13","modified_gmt":"2022-02-03T05:33:13","slug":"intro-to-linear-equations","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/02\/03\/intro-to-linear-equations\/","title":{"rendered":"Intro to Linear Equations"},"content":{"rendered":"\n

A linear equation is an equation that describes a straight line on a graph. You can remember this by the “line” part of the name linear equation. <\/p>\n\n\n\n

Standard Form <\/p>\n\n\n\n

Linear equations have a standard form that looks like this: <\/p>\n\n\n\n

Ax + By = C <\/strong><\/p>\n\n\n\n

Where A, B, and C are coefficients (numbers) while x and y are variables.<\/p>\n\n\n\n

You can think of the x and y variables as points on a graph. Example linear equations: You can plug numbers into A, B, and C of the above standard form to make linear equations: <\/p>\n\n\n\n

2x + 3y = 7 <\/p>\n\n\n\n

x + 7y = 12<\/p>\n\n\n\n

3x – y = 1 <\/p>\n\n\n\n

Linear Equations Represent Lines <\/h2>\n\n\n\n

At first it may seem strange that an equation represents a line on a graph. To make a line you need two points. Then you can draw a line through those two points. <\/p>\n\n\n\n

The x and y variables in the linear equation represent the x and y coordinates on a graph. If you plug in a number for x, you can calculate the corresponding number for y. Those two numbers show a point on a graph. If you keep plugging in numbers for x and y in a linear equation, you will find that all the points together make a straight line. <\/p>\n\n\n\n

Graphing a Linear Equation<\/h2>\n\n\n\n

In order to graph a linear equation you can put in numbers for x and y into the equation and plot the points on a graph. One way to do this is to use the “intercept” points. The intercept points are when x = 0 or y = 0. Here are some steps to follow: <\/p>\n\n\n\n

  • Plug x = 0 into the equation and solve for y <\/li>
  • Plot the point (0,y) on the y-axis <\/li>
  • Plug y = 0 into the equation and solve for x <\/li>
  • Plot the point (x,0) on the x-axis <\/li>
  • Draw a straight line between the two points <\/li><\/ul>\n\n\n\n

    You can check your answers by trying other numbers in the equation. Try x = 1. Solve for y. Then make sure that that point is on your line. <\/p>\n\n\n\n

    Example Problem:<\/h4>\n\n\n\n

    Graph the linear equation: 2x + y = 2<\/strong><\/p>\n\n\n\n

    Step 1:<\/strong> <\/p>\n\n\n\n

    Plug in x = 0 and solve for y.<\/p>\n\n\n\n

    2 (0) + y = 2 y = 2 <\/p>\n\n\n\n

    Step 2: <\/strong><\/p>\n\n\n\n

    Plug in y = 0 and solve for x. 2x + 0 = 2 2x = 2 x = 1 <\/p>\n\n\n\n

    Step 3:<\/strong> <\/p>\n\n\n\n

    Graph the x and y intercept points (0, 2) and (1,0)<\/p>\n\n\n\n

    Step 4:<\/strong> <\/p>\n\n\n\n

    Draw a straight line through the two points <\/p>\n\n\n\n

    \"\"\/<\/figure>\n\n\n\n

    Step 5: <\/strong><\/p>\n\n\n\n

    Check the answer. <\/p>\n\n\n\n

    We will put in 2 for x and solve:<\/p>\n\n\n\n

    2(2) + y = 2<\/p>\n\n\n\n

    4 + y = 2 <\/p>\n\n\n\n

    y = 2 – 4 <\/p>\n\n\n\n

    y=-2<\/p>\n\n\n\n

    Is the point (2,-2) on the line?<\/strong><\/p>\n\n\n\n

    You can try some other points to double check as well.<\/p>\n\n\n\n

    Example 2:<\/h4>\n\n\n\n

    Graph the linear equation x – 2y = 2 <\/p>\n\n\n\n

    Step 1: <\/strong><\/p>\n\n\n\n

    x = 0 0 – 2y = 2 y = -1<\/p>\n\n\n\n

    Step 2: <\/strong><\/p>\n\n\n\n

    y = 0 x – 2(0) = 2 x = 2 <\/p>\n\n\n\n

    Step 3: <\/strong><\/p>\n\n\n\n

    Graph the x and y points (0, -1) and (2,0) <\/p>\n\n\n\n

    Step 4: <\/strong><\/p>\n\n\n\n

    Draw a line through the two points<\/p>\n\n\n\n

    \"\"\/<\/figure>\n\n\n\n

    Step 5: <\/strong><\/p>\n\n\n\n

    Check your answer.<\/p>\n\n\n\n

    Let’s try x = 4<\/p>\n\n\n\n

    4 – 2y = 2<\/p>\n\n\n\n

    -2y = 2 – 4 <\/p>\n\n\n\n

    -2y = -2 <\/p>\n\n\n\n

    2y = 2 <\/p>\n\n\n\n

    y = 1 <\/p>\n\n\n\n

    Is the point (4,1) on the graph?<\/strong><\/p>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    A linear equation is an equation that describes a straight line on a graph. You can remember this by the “line” part of the name linear equation. Standard Form Linear equations have a standard form that looks like this: Ax + By = C Where A, B, and C are coefficients (numbers) while x and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[238],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/1004"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=1004"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/1004\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=1004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=1004"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=1004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}