Chapter 6

Slope

 Steepness of a line   The change in the y coordinate divided by the change in x Ϫ y Ϫ x  Ratio of the rise over run  Vertical change divided by horizontal change  Given any two coordinate points, m = (y₂- y₁) ( x₂ - x₁)

Slope Examples

 Find the slope of a line in graph form  Find the slope of a line when given two points  Find a missing coordinate when a different point, the slope is given, and one coordinate of the second point.

   

Slopes can be ….

Positive    Change in y over change in x both have the same sign As x increases y increases Positive correlation Negative    Zero Change in y over change in x have different signs As x increases, y decreases Negative correlation    No change in the y coordinate Horizontal line Zero divided by any number is zero Undefined    No change in the x-coordinate Vertical line Any number divided by zero is undefined!

More on Slope!!

 A positive slope… going up! A horizontal line…. Cross country skiing….hard work!

 A negative slope….skiing down!

vertical line…falling!

Forms of Linear Equations

 Standard Form  Ax + By = C  Solve for y  y = ??x + ?? Will learn more later  y - y₁ = m( x - x₁) Where did that come from????

recall m = (y₂- y₁) ( x₂ - x₁)

Examples with point slope form and standard form  Write an equation in point slope form for (show line)  A line that passes through (-3, 5) and has slope of 3/4  A line that passes through (0, 5) and has slope of 3  A horizontal line passing though (-6,2)  Write y +5 = -5/4(x-2) in standard form  Write and equation in point slope form and standard form for a line with points (-8,3) and (4,5)

Slope-Intercept Form

 Y = mx + b  Look familiar???

 m = slope  b = y- intercept  Easiest form to use when graphing  *** all three forms: standard, point-slope, and slope intercept are useful in different situations

Families of linear equations

Change sign of slope Change steepness of slope Change y-intercept

Parallel and Perpendicular Lines

• Parallel lines have  The same slope  Non-parallel or intersecting have  different slopes  Perpendicular lines have  opposite reciprocals as their slopes

One more formula…

 Mid point of a line in the coordinate plane