Chapter 5 Review

Slope Slope = m = = y 2 – y 1 x 2 – x 1 Example: (4, 3) & (2, -1)

Try: Find the slope 1. (5, 9) & (4, 3) 2. (3, 6) & (5, 8) 3. (7, 8) & (7, 7)

Positive Undefined Zero Negative

Example Find x given (x, 3) and (10, -3) have a slope of -6/2

Try: solve for x and y 1. (2, 7) and (3, y) have m= 4

Direct Variation Direct Variation: y = kx k = constant of variation The graph of y = kx always goes through the origin Said y varies directly to x

Steps 1. Set up y = kx form 2. Solve for k 3. New formula with only k 4. Plug in new value

Example If y varies directly to x and x = 6 when y = 30 then find x when y = 12

Try 1. If y varies directly to x and x = 4 when y = 16 then find x when y = 11

Graph Y= 3x

Slope-Intercept Form y = mx + b m = slope b = y-intercept

Graphing Three ways: 1. Put in calculator 2. Create table 3. Plot y – intercept (0, b) and then count the slope

Example y = 2x + 3

Writing an Equation in Slope Intercept Form Solve for y Example: 6x + 3y = 12

Finding the Equation in Slope Intercept Form (y = mx + b) Steps 1. Find m 2. Plug in m, x, and y 3. solve for b 4. Write equation with x and y as variables and b and m as numbers

Review: Write the equation of the line given m = 3 and b =2

Example 1: (2, 4) and m = 3

Example 3: (6, 10) and (4, 3)

Try 5. (5, 3) & (7, 2) 6. (-3, -1) & (6, -4)

Equation Forms Recap Slope Intercept Form: y = mx + b Standard Form: Ax + By = C Point Slope Form:

Finding the x and y intercepts To find the x intercept make y = 0 To find the y intercept make x = 0

Examples 1.) y= 3x + 72.) y = 4x - 5

Vertical Lines Always have the form x = # Ex.) 1.) x = 32.) x = -5

Horizontal Lines Always have the form y = # Ex. 1.) y = 42.) y = -3.5

Try: Is the line vertical or horizontal 1.) y= 32.) x = -7 3.) x = 104.) y = ¼

Parallel Lines Parallel lines: ◦ Never cross ◦ Have the same slope

Example Write the equation of a line parallel to y = 2x – 5 and through (2, 7)

Perpendicular Lines Perpendicular lines: ◦ Make a 90 degree angle ◦ Slopes are opposite reciprocals

Example Write the equation of a line perpendicular to y = 2x – 5 and through (2, 7)