Chapter 4 Graphing Graph of a Linear Function

Linear Function Fencing Company:  Fixed Charge for a Chain Link Fence Project $125  The rest of the cost for a 4 ft high fence is based on $8.50 per lineal foot of fencing.  A 6 ft high fence would be based on $13.00/ft Cost = $125 + $8.50(Length) Cost = $125 + $13.00(Length)

Cost = $125 + $8.50(Length) Cost = $125 + $13.00(Length)

Slope Slope – a ratio that describes the steepness of a line and the direction that it slants. y x   rise run 3 units 2 units

Slope – a ratio that describes the steepness of a line and the direction that it slants. y x Slope is relatively small & positive. Slope is relatively large & positive. Slope is relatively “small” & negative. Slope is relatively “large” & negative. Slope

Compute Slope when two points are known. Slope formula:   rise run

Compute the slope of this line. y x   4 – 0 4 – 3 0 – 4 3 – 4 Compute Slope

Compute the slope of this line. y x   4 – (-1) -2 – 1 -1 – 4 1 – (-2)

Compute Slope Compute the slope of a line that passes through these two points.  (-2,3) and (-6,5)

Horizontal Lines Compute the slope of this line. y x   2 – 2 5 – (- 3) y = 2 = 0

Vertical Lines Compute the slope of this line. y x   5 – (- 3) x = 4 = Undefined

Summary Horizontal lines:  Slope = 0 Vertical lines:  Slope = Undefined  0  0

Use Intercepts to Graph Lines

Intercepts Intercepts – locations where a graph intersects with an axis.   x y y - intercept x - intercept (0,5) (-6,0)

  x y y - intercept x - intercept (0,10) (8,0) Matching Excercise Intercepts

Graph with Intercepts Graph using intercepts. 3x + 2y = 12 In every x-intercept, y = 0  3x + 2(0) = 12 3x = 12 x = 4  (4,0)

Graph with Intercepts Graph using intercepts. 3x + 2y = 12 In every y-intercept, x = 0  3(0) + 2y = 12 2y = 12 y = 6   (0,6) (4,0)

Compute Intercepts Compute the x and y intercepts of this equation. 4x – 3y = 24 x – intercept (x, 0) 4x – 3(0) = 24 4x = 24 x = 6 ( 6,0 ) y – intercept (0, y) 4(0) – 3y = 24 -3y = 24 y = -8 ( 0,-8 )

Slope Intercept Form

Graph the line that passes through the point (0,2) and has a slope of m = Introduction 1 of 2 y x  (0,2)  3 ↑3 ↑ 4 → y-intercept

Introduction 2 of 2 Graph the line that passes through the point (0,-1) and has a slope of m = y x  (0,-1)  -2 ↓ 3 → y-intercept

Slope-Intercept Form Equations like these…    …are in slope-intercept format.

Slope-Intercept Form slope y-intercept = (0,2)   1 4 y-intercept

Slope-Intercept Form slope = 3 y-intercept = (0,-5)   3 1 y-intercept

Slope-Intercept Form slope y-intercept = (0,-6)   -2 3 y-intercept

Rewrite Linear Equations into Slope-Intercept Form

2x + y = 1 Rearranging Equations to Slope- Intercept Form -2x y = -2x + 1 2x + y = 1

Rearranging Equations to Slope- Intercept Form 2x + 3y = 9 -2x 3y = -2x x + 3y = 9

x – 4y = 12 Rearranging Equations to Slope- Intercept Form -x-x-x-x -4y = -x x – 4y = 12

Homework Textbook  Page 221  1-25 odd