Section 3-5 Lines in the Coordinate Plane SPI 21C: apply concept of rate of change to solve real-world problemsSPI 21D: determine the slope given a graph of a linear equations (VS)SPI 21E: determine the slope when given the coordinates of 2 pointsObjectives:

• 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

Review Slope FormulaSlope or Rate of Change

Slope = change in y change in x

Slope Formula

Slope = y2 – y1

x2 – x1

One pair ofcoordinates

The other pair of coordinates

Using Slope to graph an equationFrom known point:

Top number is rise: Move up (+) or down (-)Bottom number: Move right

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Review Slope Intercept Form

X

Yy = mx + b

f(x) slope y-intercept

Graph y = 3 x + 2 4

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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Slope Intercept Form

X

YGraph y = - 1 x – 2 2

1. Plot y-intercept

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)

X

YGraph 6x + 3y = 12

1. 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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Graph a Linear Equation in Standard Form (Graph using x and y intercepts)

X

YGraph -2x + 4y = - 8

1. Find x intercept: Substitute 0 for y; solve for x

Ax + By = C

-2x + 4(0) = - 8 -2x = - 8

x = 4

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

(4, 0)

(0, -2)

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Alternate Method to Graph Equation in Standard FormChange Equation to Slope-Intercept Form

X

YGraph -2x + 4y = - 8

1. Use Properties of Equality toSolve equation in terms of y.

Ax + By = C

-2x + 4y = - 8 +2x = - 8 + 2x

4y = 2x – 8 4 4 4 y = 1 x – 2 2

2. Plot the y-intercept: -2

(0, -2)

(2, -1)

y = mx + b

Plot the slope: ½

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Change Standard Form to Slope- Intercept Form and Graph

X

YGraph 6x + 3y = 12

1. Use properties of equality tosolve the equation in terms of y.

6x + 3y = 12 -6x = 12 – 6x

3y = -6x + 12 3 3 3 y = -2x + 4

(0, 4)

(1, 2)

2. Plot the y-intercept: 4

Plot the slope: - 2

Review: Point-slope Form of a Linear Equation

Write an equation of the line thru point P(-1, 4) with slope 3.

y – y1 = m(x – x1)

y – (4) = 3 (x – (-1)) Sub. y – 4 = 3 (x + 1) Simplify

2 Set of coordinates

(x, y) (x1, y1)

y – y1 = m(x – x1)

Substitute known values into the equation.

Write an equation of a line given two points. A(-2, 3) and B(1, -1).

m = y2 – y1 = 3 – (-1) = 4 x2 – x1 (-2) – 1 - 3

1. Find the slope.

2. Select one of the points and substitute values into equation. Pick (-2, 3).

y – y1 = m(x – x1)

y - 3 = - 4/3(x – (-2)) y – 3 = - 4/3(x + 2)

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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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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.