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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 = y2 – y1 x2 – x1 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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**Review Slope Intercept Form**

y = mx + b Y I II III IV f(x) slope y-intercept Graph y = 3 x + 2 4 X 1. Plot y-intercept 2. From known point, plot slope. (Rise over run) 3. Connect the 2 points with a line.

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**Practice II I III IV Slope Intercept Form Graph y = - 1 x – 2 2**

1. Plot y-intercept X 2. From known point, plot slope. 3. Connect the 2 points with a line.

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**Review: Standard Form of a Linear Equation (Graph using x and y intercepts)**

Ax + By = C Graph 6x + 3y = 12 Y 1. Find x intercept: Substitute 0 for y; solve for x I II III IV 6x + 3(0) = 12 6x = 12 x = 2 (0, 4) (2, 0) X 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

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Practice Graph a Linear Equation in Standard Form (Graph using x and y intercepts) Ax + By = C Graph -2x + 4y = - 8 Y 1. Find x intercept: Substitute 0 for y; solve for x I II III IV -2x + 4(0) = - 8 -2x = - 8 x = 4 (4, 0) X (0, -2) 2. Find y intercept: Substitute 0 for x; solve for y -2(0) + 4y = - 8 4y = - 8 y = - 2 3. Plot x and y intercepts: (4, 0) and (0, -2) Connect points with line

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**Alternate Method to Graph Equation in Standard Form Change Equation to Slope-Intercept Form**

Ax + By = C y = mx + b Graph -2x + 4y = - 8 Y I II III IV 1. Use Properties of Equality to Solve equation in terms of y. -2x + 4y = - 8 +2x = x 4y = 2x – 8 y = 1 x – 2 2 (2, -1) X (0, -2) 2. Plot the y-intercept: -2 Plot the slope: ½ 3. Plot x and y intercepts: (4, 0) and (0, 3) Connect points with line

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**Change Standard Form to Slope- Intercept Form and Graph**

Practice Change Standard Form to Slope- Intercept Form and Graph Graph 6x + 3y = 12 Y 1. Use properties of equality to solve the equation in terms of y. I II III IV 6x + 3y = 12 -6x = 12 – 6x 3y = -6x + 12 y = -2x + 4 (0, 4) (1, 2) X 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 a line given two points. A(-2, 3) and B(1, -1). y – y1 = m(x – x1) (x, y) (x1, y1) 1. Find the slope. 2 Set of coordinates m = y2 – y1 = 3 – (-1) = 4 x2 – x (-2) – Write an equation of the line thru point P(-1, 4) with slope 3. Substitute known values into the equation. 2. Select one of the points and substitute values into equation. Pick (-2, 3). y – (4) = 3 (x – (-1)) Sub. y – 4 = 3 (x + 1) Simplify y – y1 = m(x – x1) y – y1 = m(x – x1) y = - 4/3(x – (-2)) y – 3 = - 4/3(x + 2)

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**II I III IV Equations of Horizontal and Vertical Lines**

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

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**Practice II I III IV Equations of Horizontal and Vertical Lines**

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

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Lines in the Coordinate Plane

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