One of the most common forms of a linear equation is slope-intercept form<\/i>, which is used to describe the graph of a straight line. The formula is quickly recognizable: y<\/i> = mx<\/i> + b<\/i>. The variables y<\/i> and x<\/i> represent the coordinates of a point on the graph through which the line passes, while m<\/i> tells us what the slope of the line is and b<\/i> represents the point at which the line intersects the y<\/i>-axis.<\/p>\n
Remember: A line with a positive slope runs up and to the right (\u201cuphill\u201d), and a line with a negative slope runs down and to the right (\u201cdownhill\u201d).<\/p>\n
In the following figure, lines n<\/i> and l<\/i> have positive and negative slopes, respectively. The slope of a graph can also tell you valuable information about the rate of change of numbers and variables associated with the line. A positive slope signifies an increase in a variable, while a negative slope indicates a decrease. Large<\/i> numerical values for slope indicate rapid changes, while small<\/i> numerical values point to more gradual changes. Imagine that the balance in your checking account is B<\/i>, and that it changes with the number of days that go by, D<\/i>. Think about how each of the following models would impact your life.<\/p>\n The first equation probably looks pretty good. The second equation isn\u2019t as great. An extra quarter a day isn\u2019t going to do much for you. The third equation would quickly drive you into bankruptcy, while the fourth equation might be cause for concern after a while.<\/p>\n The y<\/i>-intercept, on the other hand, is often less significant, typically representing the initial condition in a model\u2014that is, where the model begins. In the checking account example, the beginning balance was $75 in all four models. Notice, the y<\/i>-intercept didn\u2019t change at all. \nWhich of the following shows the graph of the line y<\/i> = 4x<\/i> + 7 ? A. C. Step 1:<\/strong> Read the question, identifying and organizing important information as you go.<\/p>\n Step 2:<\/strong> Choose the best strategy to answer the question<\/p>\n Notice that the graphs are vastly different.\u00a0 You’re looking for a graph that slopes up and to the right (positive slope) and has a y<\/em>-intercept of +7.\u00a0 Only one of the graphs matches those criteria.<\/span><\/p>\n Step 3:<\/strong> Check that you answered the right<\/em> question.<\/p>\n On the PSAT Math Test, working with equations algebraically is only half the battle. The PSAT Math Test will also expect you to work with graphs of linear equations, which means using lines in slope-intercept form and point-slope form. One of the most important quantities you\u2019ll be working with when graphing a linear equation is […]<\/p>\n","protected":false},"author":1,"featured_media":28748,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[240],"tags":[195],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1709"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=1709"}],"version-history":[{"count":3,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1709\/revisions"}],"predecessor-version":[{"id":38774,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/1709\/revisions\/38774"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/28748"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=1709"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=1709"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=1709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n![](\"https:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/psat_c02_cb_02-297x300.png\")
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\nOccasionally, you will encounter a line with a slope of 0\u2014meaning it does not rise or fall from left to right. These lines are easy to spot because they are horizontal and are parallel to the x<\/i>-axis (line k<\/i> in the figure shown). Lines that are parallel to the y<\/i>-axis, such as\u00a0line m<\/i> in the figure, have slopes that are \u201cundefined.\u201d The lines themselves exist, but their slopes cannot be calculated numerically.<\/p>\n
\nPSAT Linear Graphs: Practice Question<\/h3>
\nLook at the following question to see how the PSAT might test your ability to match a linear equation with its graph.
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\n![](\"https:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/psat_c02_cb_03_3-294x300.png\")
<\/div><\/div><\/div>
\nB.
\n![](\"https:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/psat_c02_cb_04_3-294x300.png\")
<\/div><\/div><\/div><\/p><\/div>
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\n![](\"https:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/psat_c02_cb_05_3-294x300.png\")
<\/div><\/div><\/div>
\nD.
\n![](\"https:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2016\/08\/psat_c02_cb_06_3-294x300.png\")
<\/div><\/div><\/div><\/p><\/div><\/p>\n<\/div><\/div>
\nPSAT Linear Graphs: The Kaplan Method<\/h3>
\nApproach this question by using the Kaplan Method for Math.\u00a0Because there isn\u2019t any scratchwork required for a problem like this, only the column containing Kaplan\u2019s strategic thinking is included in the following table.\u00a0<\/span>Try to ask yourself similar questions as you work through questions like this on Test Day.<\/p>\nStrategic Thinking<\/h3>\n
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