ShmoopTube

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Linear Equations in Standard Form, a la Shmoop. At the Prince Charming’s ball, the princesses [Princesses gather together]

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are very concerned with standards.

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Standard number of dress sequins, standard height of a tiara… ,

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and standard form of linear equations. [Princess holding Standard Form of Linear equations book]

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How else would they plot their line past the other dancers to steal the prince on the dance

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floor? A linear equation in standard form is an equation

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that looks like this: [Linear equation in standard form example on a chalkboard]

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ax + by = c

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where a, b, and c are integers and a is non-negative

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Let’s calculate which princess is going to tackle the prince for the first dance. [princess and prince plotted on a graph]

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If Princess Eudora is at point (8, 0) and Prince Charming is at (0, 2), we can plot

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the line in between them. [plotted line between Princess Eudora and Prince Charming]

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What's the equation of this line in standard form?

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The easiest way to find the standard form of a linear equation is actually to go through [Hand rubs off writing on chalkboard]

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slope-intercept form, y = mx + b and then change it.

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The slope of the line is rise over run, or the difference between the y values divided by

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the difference in the x values.

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The y-intercept is just the value of y when x is 0. We already know that because the prince [y-intercept value written on chalkboard]

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is standing at that exact point.Now we can substitute our slope and y intercept into

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the equation…And then rearrange it into standard form by adding ¼ x to both sides

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and then multiplying both sides by 4. [1/4x added to both sides of the slope-intercept equation]

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We should end up with x plus 4y equals 8. It looks like Princess Eudora will grab the

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prince first! [Princess Eudora walking towards the Prince]

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But wait! In a game-changing move, the prince runs for the door along a line with the equation

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y minus 3x equals 2. What slope is the prince's path? [The prince walking further down the axis line]

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The first order of business is to change that equation into standard form. Well our x term can't be negative.

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Let's multiply both sides by negative 1 to get a positive x value, which gives us -y +3x = -2. We'll shift our y term to get our equation in standard form

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and wind up with 3x -y=-2

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To find the slope from the standard form of a linear equation, we can use a special formula.

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The slope of a line equals negative a over b, where a is the coefficient of x and b is [standard form of the slope equation]

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the coefficient of y.

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Since a is 3 and b is -1, the slope is negative 3 over 1, or positive 3.

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Ah, it looks like the prince has escaped and we wish him a fairytale ending. [Prince escapes from the Princess on a horse]

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Right, girls?

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