Linear Equations in Two Variables

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Presentation transcript:

Linear Equations in Two Variables Section 1.2 Linear Equations in Two Variables

What you should learn How to use slope to graph linear equations in two variables How to write linear equations in two variables How to use slope to identify parallel and perpendicular lines How to use linear equations in two variables to model and solve real-life problems

Slope describes the direction of a line.

Guard against 0 in the denominator Why is this needed? Slope If x1  x2, the slope of the line through the distinct points (x1, y1) and (x2, y2) is Guard against 0 in the denominator

Find the slope between (-3, 6) and (5, 2) x-axis y-axis Rise -4 -1 = = Run 8 2

Find the slope between (-3, 6) and (5, 2)

Find the Slope Green (3, 9) Blue (11, 2) Red (5, -2)

Find the slope between (5, 4) and (5, 2). STOP This slope is undefined.

Find the slope between (5, 4) and (5, 2). x-axis y-axis Rise -2 Undefined = = Run

Find the slope between (5, 4) and (-3, 4). STOP This slope is zero.

Find the slope between (5, 4) and (-3, 4). x-axis y-axis Rise Zero = = Run -8

From these results we can see... The slope of a vertical line is undefined. The slope of a horizontal line is 0.

Graph the line that goes through (1, -3) with x-axis y-axis (1,-3)

Using Slope to Graph Graph the line that contains (4, 5) and has a slope of 3/2. (8, 11) (6, 8) (4, 5)

Using Slope to Graph Graph (0, 8) (4, 5) (8, 2)

Slope

Point-Slope Slope Point

Slope Intercept Slope Y-intercept

Standard Form of a Line

Parallel Lines Two distinct nonvertical lines are parallel if and only if their slopes are equal. That is,

Parallel Find the slope-intercept form of the line that passes through (2,1) parallel to 2x – 3y = 5.

Perpendicular Find the slope-intercept form of the line that passes through (2,1) perpendicular to 2x – 3y = 5.

Homework Page 21 1, 9-27 odd 39- 45 odd, 51-79 odd