# Lesson 4 6 Write a linear equation in

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Lesson 4 -6 Write a linear equation in slope-intercept form Graphing a line using slope-intercept form

Various Forms of linear Equation 1 Standard Form 2 Slope-Intercept Form 3 Slope-point Form Ax + By = C y = mx + b ? m= –A B Slope y-intercept m b

2 Slope-Intercept Form y = mx + b y-intercept Slope y-intercept (b) x-intercept (a)

Write a linear equation in slope-intercept form Write the equation that describes each line in slope-intercept form 1) m = 3, b = 1 Step. 1 write the slope-intercept form Step. 2 substitute m and b 2) y = mx + b y = 3 x + 1 m = -9, b = -5/4 Step. 1 write the slope-intercept form Step. 2 substitute m and b y = mx + b y = -9 x – 5/4

3) Step. 1 write the slope-intercept form -2 (R un ) y = mx + b 4 (R ise ) Step. 2 find m and b b= – 3 Rise = +4 = – 2 m= – 2 Run Step. 3 substitute m and b y = -2 x – 3

3) m= 2; point (3, 4) is on the line Step. 1 write the slope-intercept form y = mx + b Step. 2 find b m= 2 y = mx + b 4 = 2(3) + b 4=6+b b=– 2 Step. 3 substitute m and b y = 2 x – 2 Checking (3, 4)

Graphing a line using slope-intercept form Graph the line described 1) m = -1/2, b = 3 Step. 1 graph b Step. 2 start from b, count 1 unit down and 2 units right, and plot another point. Step. 3 Draw a line through the two points b

2) y + 3 x = 1 3) Step. 1 write in slope-intercept form m y = -3 x + 1 Step. 2 graph the line b 2 y – 4 x = 0 Step. 1 write in slope-intercept form 2 y = 4 x m y = 2 x + 0 Step. 2 graph the line b b b

Real-world application: A lawyer charges a \$100 initial consultation fee plus \$30 per hour. The fee as a function of the number of hours worked is graphed below. 1) Write an equation that represents the fee as a function of hours 2) Identify the slope and the y-intercept and describe their meanings 3) Find the fee the lawyer will charge if he works for 12 hours Solution m 1) y = 30 x + 100 b 2) m = 30 The fee per hour b = 100 Fee 400 300 200 The initial fee for zero hours 100 3) y = 30(12) + 100 = \$460 2 4 6 hours 8 10

C. W / H. W 2 – 12 even + 21, 22, 24, 26, 32, 33, 34, 37, 38, 39, 40 page 272, 273, 274