2.9 Analyze Linear Equations y = mx + b PDF

2.9_ Analyze Linear Equations: y = mx + b This material may be reproduced for licensed classroom use Copyright © McGraw Hill only and may not be further reproduced or distributed. Lesson Goal ✓ graph a line from an equation in the form y = mx...

2.9_ Analyze Linear Equations: y = mx + b This material may be reproduced for licensed classroom use Copyright © McGraw Hill only and may not be further reproduced or distributed. Lesson Goal ✓ graph a line from an equation in the form y = mx + b. ✓ write an equation that represents the given graph of a line This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed. Learn Slope-Intercept Form of a Line Nonproportional linear relationships can be written in the form 𝑦 = 𝑚𝑥 + 𝑏. This is called the slope-intercept form. When an equation is written in this form, m is the slope and b is the y-intercept. The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis. This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed. Learn Slope-Intercept Form of a Line In a nonproportional linear relationship, the graph passes through the point (0, b), which is the y-intercept. You can use the slope formula to derive the equation of a line in slope-intercept form. This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  Pause and Reflect Very important P 148 1.Essential Question What is the equation of a line for a nonproportional relationship? The solution : The equation will be y = mx + b This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  Example 1 Identify Slopes and y-Intercepts Individual work 2 3 8−5 3 3 8 −3 = 5 y 2 5 5 This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  p.147 Example 2 Identify Slopes and y-Intercepts Group work The solution next page This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  p.147 The solution : equation form x 0 3 y = mx + b y -5 -4 y – intercept b=2 3 −1 2 1 1 Slope = = =− x = 0 , so , y = 0 −5 𝑦 = −5 − 2 −2 −4 2 3 So , the equation will be y = x = 3 , so , y = 1 3 −5 =1 −5 𝑦 = −4 1 3 y=− x+2 2 This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  P 148 P 149 The solution next page This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed. The solution : The solution : No one is correct because the graph is b _ y = 500 x + 100 Decreasing so the slope must be negative and x 0 1 y - intercept is 5 y 100 600 x = 0 , so , y = 500 0 + 100 𝑦 = 100 x = 1 , so , y = 500 ( 1 ) + 100 = 600 𝑦 = 600 This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  P 149 4 0 4 u p The solution : equation form y = mx + b y – intercept 1 6 b=-3 −4 −( −2) −4+2 2 1 Slope = = =− =− 2 −(−2 ) 2+2 4 2 So , the equation will be y = 1 y=− x-3 2 This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  P 149 The solution next page This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  P 149 We have two ways to solve this problem. W1. From the graph equation form y = mx + b The solution : y – intercept equation form b=6 y = mx + b 30 − 6 24 y – intercept Slope = = = 12 2 −0 2 b=4 So , the equation will be y = 12x + 6 7−1 6 6 Slope = = = =3 1 −(−1 ) 1+1 2 W2. From the given information So , the equation will be y = 12 x + 6 y = 3x + 4 This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  The solution : The solution : y=3x–5 a. y = – 5x + 25 x 0 2 b. She thought she started at 5$ y -5 1 But she started at 25$ x = 0 , so , y = 3 0 − 5 𝑦 =−5 x = 2 , so , y = 3 ( 2 ) - 5 = 6 − 5 = 1 𝑦=1 This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed. Goal #3 Apply into Real-Life situation P. 150 This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.  The solution : P. 150 a. equation form y = mx + b y – intercept , b = 12.25 33.25 −12.25 21 Slope = = = 21 1 −0 1 So , the equation will be y = 21 x + 12.25 b. From the given information We have 21 per ticket ( slope ) Plus 12.25 fee ( y – intercept ) y = 21x + 12.25 C. No, the graph should be a series of points since only whole numbers of tickets can be purchased. This material may be reproduced for licensed classroom use McGraw Hill | Slope-Intercept Form only and may not be further reproduced or distributed.