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**2.3 Linear Functions and Slope-Intercept Form**

Learning Target: I can Graph linear equations I can write equations of lines.

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**Review of Formulas Formula for Slope Point-Slope Form**

Slope-intercept Form Standard Form *where A>0 and A, B, C are integers

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Review Slope

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**Examples of linear equations**

Equation is in Ax + By =C form Rewrite with both variables on left side … x + 6y =3 B =0 … x + 0 y =1 Multiply both sides of the equation by -1 … 2a – b = -5 Multiply both sides of the equation by 3 … 4x –y =-21 2x + 4y =8 6y = 3 – x x = 1 -2a + b = 5

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**Examples of Nonlinear Equations**

The following equations are NOT in the standard form of Ax + By =C: The exponent is 2 There is a radical in the equation Variables are multiplied Variables are divided 4x2 + y = 5 xy + x = 5 s/r + r = 3

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**Find the slope of a line through points (3, 4) and (-1, 6).**

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**Write an equation for the line that passes through (-2, 5) and (1, 7):**

Find the slope: Use point-slope form:

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**Change into slope-intercept form and identify the slope and y-intercept.**

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**Change into standard form.**

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**x-intercepts and y-intercepts**

The intercept is the point(s) where the graph crosses the axis. To find an intercept, set the other variable equal to zero.

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**Horizontal Lines Slope is zero. Equation form is y = #.**

Write an equation of a line and graph it with zero slope and y-intercept of -2. y = -2 Write an equation of a line and graph it that passes through (2, 4) and (-3, 4). y = 4

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**Vertical Lines Slope is undefined. Equation form is x = #.**

Write an equation of a line and graph it with undefined slope and passes through (1, 0). x = 1 Write an equation of a line that passes through (3, 5) and (3, -2). x = 3

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**Graphing Lines graph a line. Using x and y intercepts:**

*You need at least 2 points to graph a line. Using x and y intercepts: Find the x and y intercepts Plot the points Draw your line

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**Graph using x and y intercepts**

2x – 3y = -12 x-intercept 2x = -12 x = -6 (-6, 0) y-intercept -3y = -12 y = 4 (0, 4)

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**Graph using x and y intercepts**

6x + 9y = 18 x-intercept 6x = 18 x = 3 (3, 0) y-intercept 9y = 18 y = 2 (0, 2)

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**Graphing Lines Using slope-intercept form y = mx + b:**

Change the equation to y = mx + b. Plot the y-intercept. Use the numerator of the slope to count the corresponding number of spaces up/down. Use the denominator of the slope to count the corresponding number of spaces left/right. Draw your line.

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**Graph using slope-intercept form y = -4x + 1:**

y-intercept (0, 1) Slope m = -4 = -4 1

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**Graph using slope-intercept form**

3x - 4y = 8 y = 3x - 2 4 y-intercept (0, -2) Slope m = 3 4

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Homework Homework: p. 78 #7, 11, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 43, 49, 53 Challenge - # 62

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