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Analyzing Linear Relations

Analyzing Linear Relations. Chapter 6. Slope. Steepness of a line The change in the y coordinate divided by the change in x Ϫy Ϫx Ratio of the rise over run Vertical change divided by horizontal change Given any two coordinate points, m = (y₂- y₁)

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Analyzing Linear Relations

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  1. Analyzing Linear Relations Chapter 6

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

  3. 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.

  4. Slopes can be …. • Positive • Change in y over change in x both have the same sign • As x increases y increases • Positive correlation • Negative • Change in y over change in x have different signs • As x increases, y decreases • Negative correlation • Zero • 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!

  5. More on Slope!! • A positive slope… going up! • A negative slope….skiing down! A horizontal line…. Cross country skiing….hard work! vertical line…falling!

  6. 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)

  7. 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)

  8. 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

  9. Families of linear equations Change sign of slope Change steepness of slope Change y-intercept

  10. 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

  11. One more formula… • Mid point of a line in the coordinate plane

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