SLOPE

SLOPE Slope – the measure of the steepness of a line 4 Types of Slope Positive – a line rises from left to right Negative – a line falls from left to right Zero – horizontal line Undefined – vertical line

The bigger the number is for slope, the steeper the line is. The smaller the number is for slope, the flatter the line is.

How Slope is Found Slope can be found from any two points on the line The variable or letter for slope is m Slope can be found by: m = Change in y or Subtract the y-values Change in x Subtract the x-values 2) Rise 3) Slope-intercept form Run y = mx + b

Example #1 – A line goes through the points (4,9) and (-3, 6). m= 9 – 6 = 3 4 – (-3) 7 m= 6 – 9 = -3 = 3 -3 - 4 -7 7

Examples – Find the slope of the line that goes through the two points (4,8) and (9,7) (6,4) and (5,1) (-4,-1) and (5,8) (-2,0) and (3,11) (2,5) and (7,5) (3,9) and (3,13)

Second way to find Slope 2) Rise Run Rise is on the y – axis (Up and Down) Up means a positive rise Down means a negative rise Run is on the x-axis (Left to Right) Right means a positive run Left means a negative run

Third way to find Slope Slope-Intercept Form y = mx + b m = the slope b = the y-intercept Examples y= 2x + 3 y= -7x + 5 y= ⅖x – 7 y= ⅓x 8x + y = 4 -2x + 3y = 12

Special Equaitons y = # Example: y = 5 (There is no x) Horizontal Line Slope is Zero x = # Example: x = 2 (There is no y) Vertical Line Slope is Undefined

Intercepts x-intercept – where the graph of the line crosses the x-axis y-intercept – where the graph of the line crosses the y-axis

To Find the x-intercept Substitute 0 in for y Solve for x Your intercept will be (x,0) Examples: 4x - 2y = 12 3x + 7y = 21 5x + 4y = 20 6x – 9y = 18

To Find the y-intercept Substitute 0 in for x Solve for y Your intercept will be (0,y) Examples: 4x - 2y = 12 3x + 7y = 21 5x + 4y = 20 6x – 9y = 18 Find the slope of each of these

Slope –Intercept Form y= mx + b m = slope b = y-intercept Graph these equations using y = mx + b y = ⅗ x + 4 y = -½x – 3 y = -2/5 x + 6 y = 4/3x - 2