(b) y intercept. (m) slope. Slope Intercept Form. One way to write a linear equation is in Slope Intercept Form. Slope Intercept Form.

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1 Slope Intercept Form One way to write a linear equation is in Slope Intercept Form 5 y 4 3 (b) y intercept 2 1 x (m) slope 1

2 The slope is always the change of output (y) divided by the input (x). It is also described as "rise over run". "m" It is the variable in the y =mx + b or slope intercept form. SLOPE (m) Constant Rate of Change The slope is always the change of output (y) divided by the input (x). It is also described as "rise over run". It is the variable "m" in the y =mx + b or slope intercept form. Slope NO Slope NO Slope Slope Slope NO Slope NO Slope NO Slope NO Slope Slope Slope Slope 2

3 Y INTERCEPT The intersecting point on the y axis The y intercept is always on the y axis. It is the "b" variable "b" in the y =mx + b or b slope intercept form. b b b b b b 3

4 SLOPE Y INTERCEPT FORM (y = mx + b) y = m x + b variable y axis dependent output (y) ryse (,y) range coefficient KROC variable x axis constant y intercept (k in direct variation) independent (0,b) or (0,y) ROC input (x) intersection on y axis ryse per run run flat fee slope ( x, ) constant number domain no rate attached (constant rate of change) y 2 y 1 x 2 x 1 4

5 SLOPE Y INTERCEPT FORM (y = mx + b) y = m x + b y 2 y 1 x 2 x 1 5

6 SLOPE Y INTERCEPT FORM (y = mx + b) Identify the slope and y intercept of the equation y = 4x + 3 m = 4 b = 3 y = 4x + 3 (0,3) Find the "m" & "b" values from the y = mx + b form y = x 6 m = 1 b = 6 y = 1x 6 (0, 6) 6

7 SLOPE Y INTERCEPT FORM (y = mx + b) Given the graph, write the slope intercept form 1) Find where the line crosses the y axis = "b" (0,1) 2) Find another point on the line (fit perfect in middle of the intersection of x and y axis) 3) Count the ryse 4 4) Count the run 1 5) Divide the ryse/run (m)and simplify 4 6) Look for the + or direction of the line and insert in front of m 7)Substitute m & b into the y = mx + b form y = 4x + 1 run 1 ryse run 4y intercept 1 ryse "b" 7

SLOPE Y INTERCEPT FORM (y = mx + b) Given the graph, write the slope intercept form 1) Find where the line crosses the y axis = "b" (0,3) 2) Find another point on the line (fit perfect in middle of

8 SLOPE Y INTERCEPT FORM (y = mx + b) Given the graph, write the slope intercept form 1) Find where the line crosses the y axis = "b" (0,3) 2) Find another point on the line (fit perfect in middle of the intersection of x and y axis) 3) Count the ryse 24) Count the run4 5) Divide the ryse/run (m)and simplify 6) Look for the + or direction of the line and insert in front of m ) Substitute m & b into the y = mx + b form y = x

9 PRACTICE (y = mx + b) Identify the slope and y intercept of the equation y = 3x 2 y = 7x + 9 y = x + 2 9

10 PRACTICE (y = mx + b) Given the slope and y intercept, write the equation m = 5 b = 9 m = 2 b = 8 m = b = 17 10

11 PRACTICE (y = mx + b) Given the graph, write the slope intercept form 11

12 PRACTICE (y = mx + b) Given the graph, write the slope intercept form 12

13 PRACTICE (y = mx + b) Given the graph, write the slope intercept form 13

14 1 Calculate the slope 2 Find the y intercept 3 Write the equation of the line in the Slope Intercept Form Push the shade to find the answer Hint: Teacher will change the slope and the y intercept and repeat the question as many times as the students need to practice. 14

15 Draw a line through the point (1,2) with the slope of -3/2 First plot the point on a coordinate plane. Find another point using slope -3/2 (remember what does -3/2 as the slope mean?) Draw a line through the points! 15

16 Try this! Graph the line through the point (2,-3) with slope 5/4 16

17 Pull When given an equation such as y=mx+b slope is the coefficient to x. (m) ALWAYS! Dependent/independent variable? 17

18 What is the slope of the given equation (function)? y = 4x + 6 m = 4 y = 1/3x 9 m = 1/3 18

19 y = x + 3/4 m = 1 4x + 2y = 16 4x = 4x y = 4x y = 2x + 8 m = 2 19

20 2x + y = 8 2x = 2x + 8 y = 2x + 8 m = 2 y = 2 + 5x y = 5x 2 m = 5 20

21 RECAP! How do you find slope if you are given a graph? How do you find slope if you are given an equation? What might you have to do to the equation first? How do you find slope if given two points from the line? What do the little 2's & 1's mean in the slope formula? 21

Move the rectangle to see the answer 2 1 2 3 4 5 6 7 8 Height (minutes) xt Slope= = = 0.125 The graph crosses the vertical axis at (0,8).

22 Real World Problem The graph shows the height of a candle as it burns. Find the slope and the vertical intercept of the graph. Write h Height (cm) y (0,8) (8,7) an equation for the height 4 of the candle in Slope 3 Intercept Form. Move the rectangle to see the answer Height (minutes) xt Slope= = = The graph crosses the vertical axis at (0,8). The vertical intercept is 8 Let h = the height of the candle in centimeters after it has been burning t minutes An equation for the height of the candle is h = t

23 Check your knowledge Remember: The equation of the line in the slope intercept form is y = m x + b *Grandal (2009).This test copied from ihs_graphing retrived from : 23

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