2.3 slope and 2.4 writing linear equation

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Presentation transcript:

2.3 slope and 2.4 writing linear equation Algebra II w/ trig

Slope(m) is the ratio change in a vertical direction to the corresponding change in the horizontal direction. m = Where (x1  x2)

The line rises to the right. 2. Zero The line is horizontal. Type of Slope Description of Graph Sketch 1. Positive The line rises to the right. 2. Zero The line is horizontal. 3. Negative The line falls to the right. 4. Undefined The line is vertical. Special types of lines: Parallel lines have the same slope. Perpendicular lines have opposite reciprocal slopes.

I. Find the slope given two ordered pairs and graph. A. (1, 3) and (-2, -3) B. (2, 3) and (-1, 5)

II. Graph 1. has slope of -3/4 and passing through (1, -3)

2. has slope of -3 and passing through (2, 5)

III. Tell whether the lines are parallel, perpendicular, or neither. A III. Tell whether the lines are parallel, perpendicular, or neither. A. Line 1: (-3, 3) and (3, -1) Line 2: (-2, -3) and (2, 3) B. Line 1: (5,-10) and (6, 5) Line 2: (3, 4) and (-5,-4)

2.4 Writing Linear equations Slope Intercept Form of a Linear Equation: y = mx + b, where m is the slope and b is the y intercept (0, b). This is a quick way to graph equation. Graphing equations in slope intercept form: 1. solve for y 2. find y-intercept 3. use slope 4. draw line through points

I. Graph A. B. 2x + 3y = 12

C. x = -3 D. y = -4

E. Graph the line through (2, 3) that is parallel to the line with the equation 3x + y = 6

F. Graph the line through (2, 1) that is perpendicular to the line with the equation 2x – 3y = 3

II. Write an equation in slope-intercept form for each graph.

B.

C.

III. Write an equation in slope intercept form for the line with the given info. A. Given Two Points: Steps: Find the slope. Find the y-intercept (using the slope and one of the points, solve y=mx + b for b) Write the equation, by plugging the slope and the y- intercept into y=mx + b. 1. (4, -3), (2, 1)

2. (-2, 8), (-2, 1) 3. x-int: 3; y-int: 2

B. Given a point and an equation. Steps: Find the slope of the equation. Find the y- intercept, using the slope and the given point. Write the equation. (Remember parallel= same slope, perpendicular = opposite reciprocal slope. 1. contains (-1, 3) and is parallel to graph y = -2x + 4

2. contains (4, -3) and is parallel to graph 3x + 4y = 8

3. contains (-4, -3) and is perpendicular to y = 4x + 5

4. contains (-2, 4) and is perpendicular to x – 6y = 15