By Matty Lu and Mc-Welch Linear Equations By Matty Lu and Mc-Welch

Basics Slope-Intercept Form y = mx + b m = slope b = y-intercept Ex. y = 2/3x + 2 slope = 2/3 y-intercept = 2

Slope y = mx + b slope= rise/run slope = y = y2-y1 x x2-x1 Ex. (-3,0) (3,4) slope= 4 - 0 = 2 3-(-3) 3

y-intercept y = mx + b Ex. (3,4) m= 2/3 4=(2/3)(3) + b 4 = 2 + b 2 = b b = x-value at which line crosses y-axis Plug in coordinates for x and y Plug in slope for m Solve for b Ex. (3,4) m= 2/3 4=(2/3)(3) + b 4 = 2 + b 2 = b

Example 1 Write in slope-intercept form the equation of the line that passes through the given points. Ex. 1. (6,2) , (8,-4) Step 1 -4 –2 = -3 8 - 6 Final Step y = mx + b y = -3x + 20 Step 2 y = mx + b 2 = (-3)6 + b b = 20

Example 2 Using the graph, identify y-intercept and slope and put into slope-intercept form y-intercept = 1 slope = -4 y = -4x + 1

Example 3 Between 1995-2001, a company’s profits decreased by about $1200 per year. In 1997, the company had an annual profit of $1,500,000. Write an equation that gives the annual profit P in terms of the year t. Let t=0 represent 1995.

Example 3 (cont.) Step 1: Identify key values Step 3: Write equation x = years (t) y = $profit (P) slope = -$1200/yr point (2, 1500000) with 2 representing the year 1997 Step 3: Write equation y = mx + b y = -1200x + 1502400 Step 2: Substitute values into equation, and solve for b y = mx + b 1500000 = (-1200)(2) + b b = 1502400

Extra Problems Write equation using the Click for the answers. given information. m = 4, b = -2 m = -5, b = 3 (2, 6), m = 2 4. (3, -9), m = -5 5. (-2, 5), (2, 4) 6. (9, -1), (1, -9) Click for the answers. 1. y = 4x – 2 2. y = -5x + 3 3. y = 2x + 2 4. y = -5x + 6 5. y = -1/4x + 9/2 6. y = x – 10

Website Links - explanations For additional practice go to the following website, www.classzone.com.