Geometry Today: Check Up 3.4 Instruction Practice

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Presentation transcript:

Geometry Today: Check Up 3.4 Instruction Practice Never discourage anyone who continually makes progress… no matter how slow. Plato

Chapter 3 Check Up For 1 – 3, refer to the figure.

3.4 Equations of Lines Objectives: Vocabulary: Find the slope of lines Find slope of parallel and perpendicular lines Find equations of lines using y = mx + b Find equations of lines using y – y1 = m(x – x1) Write the equation of parallel lines Vocabulary: slope, slope intercept form, point-slope form

3.3 Slopes of Lines Formula: Slope rules: Parallel Lines: Perpendicular Lines: Parallel Lines: same slope opposite reciprocal slope 0 slope: horizontal line y = # Undefined slope: vertical line x = #

3.4 Equations of Lines y-intercept (0, b) slope Formulas: slope-intercept form y-intercept (0, b) slope Need slope (m) to find parallel and perpendicular from equation.

Are these lines parallel, perpendicular or neither?

Are these lines parallel, perpendicular or neither? y = 3x – 6 y = 3x+ 4 y = 1/5x + 4 y = 5x – 1/4 4y = 8x + 12 y = -1/2 x + 4 Perpendicular Need slope (m) to find parallel and perpendicular from equation.

slope y - y1=m(x - x1) point (x1, y1) Formulas: point-slope form slope y - y1=m(x - x1) y1 x1 point (x1, y1) Used to find the equation of a line find slope, m, and a point (x1, y1) plug values into the equation distribute and add

y – 5 = 3 (x - 2) y - y1=m(x - x1) x1 y1 x1 y1 m x1 y1 Perp m m = +½ Find the equation of the line through (2, 5) and m = 3. y – 5 = 3 (x - 2) y - y1=m(x - x1) x1 y1 Still distribute and add Find the equation of the line through (0, 3) and parallel to y = 3x + 9. Find the equation of the line through (4, -1) and perpendicular l to y = -2x – 1. x1 y1 m x1 y1 Perp m m = +½

Are the 2 lines parallel, perpendicular, or neither? y = -2/3 x – 3 y = 2/3x + 5 3y + 4x = 24 4y – 3x = 12 4y + 3x = 15 12x + 9y = 36 Perp

Find the equation of the line through (4, 5) and m = 6. Find the equation of the line through (3, 7) and parallel to line from #1. Find the equation of the line through (-2, 4) and perpendicular to line from #1. Find the equation of the line through (-2, 4) and perpendicular to line y = 2x -7.

Yesterday Assignment: 3.4 p. 203 #37-55 odd, 59-61 all Never discourage anyone who continually makes progress… no matter how slow. Plato