4.6 Slope Intercept Form And Parallel Lines

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Presentation transcript:

4.6 Slope Intercept Form And Parallel Lines Algebra 4.6 Slope Intercept Form And Parallel Lines

You have already learned an easy method of graphing that uses only the y-intercept (b) and the slope (m).

Let’s review . . . .

Slope-Intercept Form y = mx + b slope y-intercept rise run where the line crosses the y axis

Converting to Slope-Intercept Form (y = mx + b) Convert: 4x – 5y = 15 -4x -4x -5y = -4x + 15 -5 -5

Converting to Slope-Intercept Form (y = mx + b) Convert: 4x – 5y = 15 -4x -4x -5y = -4x + 15 -5 -5 Now let’s graph this equation.

.(0,-3) Graph the y-intercept The y intercept of the line is -3. Plot the point (0,-3) on the y axis. .(0,-3) x

. (10,5) . (5,1) .(0,-3) Using the slope to find more points Rise 4 y . (10,5) . (5,1) The slope of the line is or x .(0,-3) Rise 4 Run 5 From the y intercept of (0,-3) rise 4, run 5, plot, repeat. Then connect for the line.

Parallel Lines Parallel lines in the same plane do not intersect Horizontal lines are parallel to other horizontal lines Vertical lines are parallel to other vertical lines Sloped lines (uphill and downhill) are parallel to each other if they have the same slope

Horizontal Lines Horizontal lines all have a slope of 0. y Horizontal lines are all parallel to each other. y = 5 y = 3 x y = -2 y = -6 Horizontal lines all have a slope of 0.

Vertical Lines Vertical lines all have a slope that is UNDEFINED. y x = 3 x = 5 x = -6 x = -2 Vertical lines are all parallel to each other. x Vertical lines all have a slope that is UNDEFINED.

Sloped Lines Sloped lines are y = 2x + 4 y = 2x + 1 y Sloped lines are all parallel to each other if they have the same slope. y = 2x - 2 y = 2x - 5 x

Sloped Lines y = -½x + 4 y = -½x y = -½x -3 y = -½x - 4 Sloped lines are all parallel to each other if they have the same slope. y = -½x + 4 x y = -½x y = -½x -3 y = -½x - 4

Check for Understanding Which of the following lines are parallel? (Hint: convert to slope-intercept form and compare slopes) 3y = -9x – 5 2y – 6x = -5 12x + 4y = 1 Answer: Lines a and c are parallel. They both have a slope of -3.

Homework pg. 245 #46-55, 60-61, 66-68 pg. 247 Quiz 2 all