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Section 3-5 Lines in the Coordinate Plane SPI 21C: apply concept of rate of change to solve real-world problems SPI 21D: determine the slope given a graph of a linear equations (VS) SPI 21E: determine the slope when given the coordinates of 2 points Objectives: Graph lines given their equations Write equations of lines Linear Equation: equation of a line all points on the line are a solution to the equation Forms of Linear Equations: Slope-Intercept Standard Form Point-slope Form

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Review Slope Formula Slope or Rate of Change Slope = change in y change in x Slope Formula Slope = y 2 – y 1 x 2 – x 1 One pair of coordinates The other pair of coordinates Using Slope to graph an equation From known point: Top number is rise: Move up (+) or down (-) Bottom number: Move right

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0 Review Slope Intercept Form X Y y = mx + b f(x)slopey-intercept Graph y = 3 x Plot y-intercept 2. From known point, plot slope. (Rise over run) 3. Connect the 2 points with a line.

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0 Slope Intercept Form X Y Graph y = - 1 x – Plot y-intercept 2. From known point, plot slope. 3. Connect the 2 points with a line.

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0 Review: Standard Form of a Linear Equation (Graph using x and y intercepts) X Y Graph 6x + 3y = Find x intercept: Substitute 0 for y; solve for x Ax + By = C 6x + 3(0) = 12 6x = 12 x = 2 2. Find y intercept: Substitute 0 for x; solve for y 6(0) + 3y = 12 3y = 12 y = 4 3. Plot x and y intercepts: (2, 0) and (0, 4) Connect points with line (2, 0) (0, 4)

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0 Graph a Linear Equation in Standard Form (Graph using x and y intercepts) X Y Graph -2x + 4y = Find x intercept: Substitute 0 for y; solve for x Ax + By = C -2x + 4(0) = x = - 8 x = 4 2. Find y intercept: Substitute 0 for x; solve for y -2(0) + 4y = - 8 4y = - 8 y = Plot x and y intercepts: (4, 0) and (0, -2) Connect points with line (4, 0) (0, -2)

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0 Alternate Method to Graph Equation in Standard Form Change Equation to Slope-Intercept Form X Y Graph -2x + 4y = Use Properties of Equality to Solve equation in terms of y. Ax + By = C -2x + 4y = x = x 4y = 2x – y = 1 x – Plot the y-intercept: Plot x and y intercepts: (4, 0) and (0, 3) Connect points with line (0, -2) (2, -1) y = mx + b Plot the slope: ½

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0 Change Standard Form to Slope- Intercept Form and Graph X Y Graph 6x + 3y = Use properties of equality to solve the equation in terms of y. 6x + 3y = 12 -6x = 12 – 6x 3y = -6x y = -2x + 4 (0, 4) (1, 2) 2. Plot the y-intercept: 4 Plot the slope: - 2

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Review: Point-slope Form of a Linear Equation Write an equation of the line thru point P(-1, 4) with slope 3. y – y 1 = m(x – x 1 ) y – (4) = 3 (x – (-1)) Sub. y – 4 = 3 (x + 1) Simplify 2 Set of coordinates (x, y) (x 1, y 1 ) y – y 1 = m(x – x 1 ) Substitute known values into the equation. Write an equation of a line given two points. A(-2, 3) and B(1, -1). m = y 2 – y 1 = 3 – (-1) = 4 x 2 – x 1 (-2) – Find the slope. 2. Select one of the points and substitute values into equation. Pick (-2, 3). y – y 1 = m(x – x 1 ) y - 3 = - 4/3(x – (-2)) y – 3 = - 4/3(x + 2)

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0 Equations of Horizontal and Vertical Lines X Y (0, 3) Graph the equation y = 3. For all values of x in the graph of y = 3, what is the value of y? Graph a Horizontal Linear Equation 1. Plot the point (0, 3) 2. Draw a horizontal line.

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0 Equations of Horizontal and Vertical Lines X Y (4, 0) Graph the equation x = 4. For all values of y in the graph of x = 4, what is the value of x? Graph a Vertical Linear Equation 1. Plot the point (4, 0) 2. Draw a vertical line.

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