{"id":1006,"date":"2022-02-05T05:07:31","date_gmt":"2022-02-05T05:07:31","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=1006"},"modified":"2022-02-05T05:07:31","modified_gmt":"2022-02-05T05:07:31","slug":"linear-eq-slope-forms","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/02\/05\/linear-eq-slope-forms\/","title":{"rendered":"Linear Eq. &#8211; Slope Forms"},"content":{"rendered":"\n<p>This page assumes you have some basic knowledge of linear equations and slope. In the linear equations basics section we discussed the standard form of a linear equation where Ax + By = C.<\/p>\n\n\n\n<p> There are other ways that linear equations can be written that can help provide useful information for graphing. They are called slope forms. There is the slope-intercept form and the point-slope form. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"slope-intercept-form\">Slope-Intercept Form <\/h2>\n\n\n\n<p>The slope intercept form uses the following equation:<\/p>\n\n\n\n<p> <strong>y = mx + b <\/strong><\/p>\n\n\n\n<p>In this equation, x and y are still the variables. <\/p>\n\n\n\n<p>The coefficients are m and b. These are numbers. <\/p>\n\n\n\n<p>The advantage of putting a linear equation in this form is that the number for m equals the slope and the number for b equals the y-intercept. This makes the line the equation represents simple to graph.<\/p>\n\n\n\n<p> m = slope <\/p>\n\n\n\n<p>b = intercept <\/p>\n\n\n\n<p>slope = (change in y) divided by the (change in x) = (y2 &#8211; y1)\/(x2 &#8211; x1)<\/p>\n\n\n\n<p> intercept = the point where the line crosses (or intercepts) the y-axis<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"example-problems-1\"> Example Problems:<\/h4>\n\n\n\n<p id=\"example-problems-1\"><strong> 1) Graph the equation y = 1\/2x + 1 <\/strong><\/p>\n\n\n\n<p>From the equation y = mx + b we know that: <\/p>\n\n\n\n<p>m = slope = \u00bd <\/p>\n\n\n\n<p>b = intercept = 1 <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.ducksters.com\/kidsmath\/slope_intercept_graph.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p>1)Graph the equation y = 3x &#8211; 3 <\/p>\n\n\n\n<p>From the equation y = mx + b we know that: <\/p>\n\n\n\n<p>m = slope = 3<\/p>\n\n\n\n<p> b = intercept = -3 <\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.ducksters.com\/kidsmath\/slope_intercept_graph2.gif\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"point-slope-form\">Point-Slope Form <\/h2>\n\n\n\n<p>The point-slope form of linear equation is used when you know the coordinates of one point on the line and the slope. The equation looks like this: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>y &#8211; y1 = m(x &#8211; x1) <\/strong><\/p>\n\n\n\n<p>y1, x1 = the coordinates of the point you know<\/p>\n\n\n\n<p> m = the slope, which you know<\/p>\n\n\n\n<p>x, y = variables<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"example-problems\"> Example Problems: <\/h4>\n\n\n\n<p>Graph a line that passes through the coordinate (2,2) and has a slope of 3\/2. Write the equation in the slope-intercept form. <\/p>\n\n\n\n<p>See the graph below. First we plotted the point (2,2) on the graph. Then we found another point using a rise of 3 and a run of 2. We drew a line between these two points.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.ducksters.com\/kidsmath\/slope_point_linear_equation_graph.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p> To write this equation in slope-intercept form we use the equation: <\/p>\n\n\n\n<p>y = mx + b <\/p>\n\n\n\n<p>We already know that the slope (m) = 3\/2 from the question. The y-intercept (b) we can see is at -1 from the graph. We can fill in m and b to get the answer: <\/p>\n\n\n\n<p>y = 3\/2x -1 <\/p>\n\n\n\n<p><strong>Things to Remember <\/strong><\/p>\n\n\n\n<ul><li>Slope-intercept form is y = mx + b. <\/li><li>Point-slope form is y &#8211; y1 = m(x &#8211; x1). <\/li><li>We can write a linear equation in three different ways: standard form, slope-intercept form, and point-slope form.<\/li><\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This page assumes you have some basic knowledge of linear equations and slope. In the linear equations basics section we discussed the standard form of a linear equation where Ax + By = C. There are other ways that linear equations can be written that can help provide useful information for graphing. They are called [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[852],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/1006"}],"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=1006"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/1006\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=1006"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=1006"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=1006"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}