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Graphing Linear Equations

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Identifying a Linear Equation A linear equation is any equation that can be put in the form... Ax + By = C... where A, B, and C are real numbers, and A and B are not both zero. The graph of a linear equation is a line. Which of the following equations are linear equations? 3x + y = 82(x + 3)(x + 4) = y 2x 2 + 3x + 4 = y5y + x = 1 –3x 2 – y = 98x – 3x + x – 4 = y

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The Graph of a Linear Equation One way to graph a linear equation: Make a table of at least three ordered pairs Plot the points (x, y) on a coordinate grid. Connect the points with a straight line. Complete the table of values for y = 3x + 1, then graph the ordered pairs on a coordinate grid. xy –2 0 2 that make the equation true.

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The Graph of a Linear Equation One way to graph a linear equation: Make a table of at least three ordered pairs Plot the points (x, y) on a coordinate grid. Connect the points with a straight line. Complete the table of values for y = 3x + 1, then graph the ordered pairs on a coordinate grid. xy –2–5 01 27 that make the equation true.

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The Slope of a Linear Equation To find the slope, m, of a graphed line, you need: any two points on the line: (x, y ) and (x, y ) to write and simplify the following ratio: 2211 What is the slope of 3x + y = 8? m = (y 2 – y 1 ) (x 2 – x 1 ) rise run =

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The Slope of a Linear Equation To find the slope, m, of a graphed line, you need: any two points on the line: (x, y ) and (x, y ) to write and simplify the following ratio: 2211 What is the slope of 3x + y = 8? m = –3 m = (y 2 – y 1 ) (x 2 – x 1 ) rise run =

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Forms of a Linear Equation Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept Point-Slope Form: y – y = m(x – x ), where m is the slope and Write y – 1 = 3x in Slope-Intercept form. 11 11 Find the slope and the y-intercept. Use the Point-Slope form to write the equation for the line that passes through points (1, 3) and (–11, –5) in Ax + By = C form. x and y are the coordinates for any point on the line

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Forms of a Linear Equation Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept Point-Slope Form: y – y = m(x – x ), where m is the slope and Write y – 1 = 3x in Slope-Intercept form. 11 11 Find the slope and the y-intercept. Use the Point-Slope form to write the equation for the line that passes through points (1, 3) and (–11, –5) in Ax + By = C form. y = 3x + 1; m = 3; y-intercept is 1 2x – 3y = –7 x and y are the coordinates for any point on the line

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