Transcript Analyzing Linear Relations Chapter 6
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)
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!
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)
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