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# LINEAR FUNCTIONS

A simplified lesson plan presentation that explain in detail linear functions and gives examples along with extra- practice.

by

Tweet## Jasmine Asad

on 17 March 2013#### Transcript of LINEAR FUNCTIONS

An Overview LINEAR FUNCTIONS: *Define linear functions.

*Identify parent function.

*Examine 3 types of linear

equations.

*Find slope.

*Differentiating between

perpendicular/parallel lines.

*Write equations passing

through points.

*Graph linear equations. Objectives Parent Function > y=x Linear Function: a function with a line graph. Change of y SLOPE PARALLEL V.S PERPENDICULAR LINES By: Jasmine Asad

Grade 10C Vocabulary linear function

slope

y-intercept

x-intercept

point-slope form

standard form

slope-intercept form

linear term

constant Define y-intercept: point that intersects the y-axis x-intercept: point that intersects the x-axis (0,0) Change of x OR Rise Run Determines how slanted a line is. To find slope using 2 points: (y2-y1) (x2-x1) Example: Find the slope of line with the points (1,5) and (0,2) (y2-y1) (x2-x1) Plug in co-ordinates Example: Find the slope of line with the points (1,5) and (0,2) (y2-y1) (x2-x1) Plug in co-ordinates (5-2) (1-0) Simplify m= m= m=3 DIFFERENTIATE PARALLEL: PERPENDICULAR: Used in non-vertical lines. *Same slope

*May have diff. y-intercept Example: Write an equation of the line passing through (-2,1) and ll to y=-3x + 1 1- Plug in same slope and the co-ordinates. 1=-3(2) + b 2- Solve for b to get the y-intercept. 1= 6 + b

1-6 = b

-5= b 3- Re-write the final new equation including the y-intercept. y= -3x - 5 *Slope= reciprocal + opposite signs

*May have diff. or same y-intercept Example: Write an equation of the line passing through (-3,-1) and to y=-2x - 4 1- Plug in slope with opposite sign and reciprocal

and the co-ordinates given. 2- Solve for b to get the y-intercept. 3- Re-write the final new equation including the y-intercept. 5 5 -1 = 5 (-3) + b 2 -1 = -15 + b 2 -1 + 15 = b 2 13= b 2 y= 5x + 13 2 2 3 FORMS OF LINEAR EQUATIONS SLOPE-INTERCEPT STANDARD Y mx + b EQUATION = mx = linear term + b = constant CONTENTS: *Advantage:

-MOSt Common Equation used for Graphing

-Can be converted from standard and point-slop form. y-y1 m (x-x1) EQUATION = CONTENTS POINT SLOPE POINT - SLOPE *ADVANTAGE :

Easy to have a point and slope plugged into

or just 2 points. ax + by c EQUATION = *ADVANTAGE:

-Can be converted to slope-intercept form.

-Can be graphed using the x and y-intercepts.

-The a variable has to be a real number (not negative or less than 0. ) EXAMPLE: Write in A) Point Slope form, B) Slope intercept form, and C)Standard form the Equation of the line that passes through (-3,5) with slope of -1, then D) Graph. EXAMPLE: Write y= 1.5x + 4 in Standard form 1- Move the (1.5x) to the other side -1.5x + y=4 2- Multiply the equation by -2 to make the a a real number. {-1.5x + y=4} x-2 3- Re- write the equation. 3x - 2y = -8 EXAMPLE: Using the points (1,9) and (6,2), write an equation ins point slope form. 1- Find slope using: y2-y1 x2-x1 9-2 1-6 = -7 5 2- Choose a point to plug in along with the slope: y-2= -7 (x-6) 5 EXAMPLE: Write the equation of the line that passes through (0,2) with a slope of 5 in slope intercept form 1-Plug in slope and co-ordinates: 2= 5(0) + b 2-Solve for b: 2= b 3-Re-write the equation incorporating the slope

and y-intecept: y= 5x + 2 Point- Slope Form Slope Intercept Form Standard Form GRAPH : y-y1 = m(x-x1) y-5 = -1(x+3) y-5 = -1(x+3) y-5 = -1x-3 y = -1x-3 + 5 y = -x + 2 y = -x + 2 x + y = 2 VERTICAL LINEs HORIZONTAL LINES *y = b

*m = 0

*y is constant *X = C

*m = undefined

*x is constant EXAMPLE : x = 3 EXAMPLE : y = 3 CLASSWORK Page 68 : # 20 - 50 even

Page 110 : #14- 19

Full transcript*Identify parent function.

*Examine 3 types of linear

equations.

*Find slope.

*Differentiating between

perpendicular/parallel lines.

*Write equations passing

through points.

*Graph linear equations. Objectives Parent Function > y=x Linear Function: a function with a line graph. Change of y SLOPE PARALLEL V.S PERPENDICULAR LINES By: Jasmine Asad

Grade 10C Vocabulary linear function

slope

y-intercept

x-intercept

point-slope form

standard form

slope-intercept form

linear term

constant Define y-intercept: point that intersects the y-axis x-intercept: point that intersects the x-axis (0,0) Change of x OR Rise Run Determines how slanted a line is. To find slope using 2 points: (y2-y1) (x2-x1) Example: Find the slope of line with the points (1,5) and (0,2) (y2-y1) (x2-x1) Plug in co-ordinates Example: Find the slope of line with the points (1,5) and (0,2) (y2-y1) (x2-x1) Plug in co-ordinates (5-2) (1-0) Simplify m= m= m=3 DIFFERENTIATE PARALLEL: PERPENDICULAR: Used in non-vertical lines. *Same slope

*May have diff. y-intercept Example: Write an equation of the line passing through (-2,1) and ll to y=-3x + 1 1- Plug in same slope and the co-ordinates. 1=-3(2) + b 2- Solve for b to get the y-intercept. 1= 6 + b

1-6 = b

-5= b 3- Re-write the final new equation including the y-intercept. y= -3x - 5 *Slope= reciprocal + opposite signs

*May have diff. or same y-intercept Example: Write an equation of the line passing through (-3,-1) and to y=-2x - 4 1- Plug in slope with opposite sign and reciprocal

and the co-ordinates given. 2- Solve for b to get the y-intercept. 3- Re-write the final new equation including the y-intercept. 5 5 -1 = 5 (-3) + b 2 -1 = -15 + b 2 -1 + 15 = b 2 13= b 2 y= 5x + 13 2 2 3 FORMS OF LINEAR EQUATIONS SLOPE-INTERCEPT STANDARD Y mx + b EQUATION = mx = linear term + b = constant CONTENTS: *Advantage:

-MOSt Common Equation used for Graphing

-Can be converted from standard and point-slop form. y-y1 m (x-x1) EQUATION = CONTENTS POINT SLOPE POINT - SLOPE *ADVANTAGE :

Easy to have a point and slope plugged into

or just 2 points. ax + by c EQUATION = *ADVANTAGE:

-Can be converted to slope-intercept form.

-Can be graphed using the x and y-intercepts.

-The a variable has to be a real number (not negative or less than 0. ) EXAMPLE: Write in A) Point Slope form, B) Slope intercept form, and C)Standard form the Equation of the line that passes through (-3,5) with slope of -1, then D) Graph. EXAMPLE: Write y= 1.5x + 4 in Standard form 1- Move the (1.5x) to the other side -1.5x + y=4 2- Multiply the equation by -2 to make the a a real number. {-1.5x + y=4} x-2 3- Re- write the equation. 3x - 2y = -8 EXAMPLE: Using the points (1,9) and (6,2), write an equation ins point slope form. 1- Find slope using: y2-y1 x2-x1 9-2 1-6 = -7 5 2- Choose a point to plug in along with the slope: y-2= -7 (x-6) 5 EXAMPLE: Write the equation of the line that passes through (0,2) with a slope of 5 in slope intercept form 1-Plug in slope and co-ordinates: 2= 5(0) + b 2-Solve for b: 2= b 3-Re-write the equation incorporating the slope

and y-intecept: y= 5x + 2 Point- Slope Form Slope Intercept Form Standard Form GRAPH : y-y1 = m(x-x1) y-5 = -1(x+3) y-5 = -1(x+3) y-5 = -1x-3 y = -1x-3 + 5 y = -x + 2 y = -x + 2 x + y = 2 VERTICAL LINEs HORIZONTAL LINES *y = b

*m = 0

*y is constant *X = C

*m = undefined

*x is constant EXAMPLE : x = 3 EXAMPLE : y = 3 CLASSWORK Page 68 : # 20 - 50 even

Page 110 : #14- 19