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Understanding Slope and Y-Intercept in Linear Equations: Insights on m and b

This exploration delves into the components of linear equations in the slope-intercept form, represented as y = mx + b. Here, 'm' denotes the slope of the line, indicating the rate of change, while 'b' signifies the y-intercept—the point where the line crosses the y-axis. By analyzing various linear equations, we reveal patterns in data tables, calculate slopes, and derive meaningful interpretations of these parameters. Understanding these elements aids in visualizing linear relationships and their real-world applications.

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Understanding Slope and Y-Intercept in Linear Equations: Insights on m and b

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Presentation Transcript

  1. Y-int Slope Form y = mx + b What does the m and b represent?

  2. Exploring the m • We already know that in a table of values for a linear relationship a pattern will form. This pattern is the rate of change. • Pattern → up by 2 Equation → y = 2x + 8

  3. Exploring the m • What is the pattern? • Pattern → down by 3 • What is the equation? Equation → y = -3x + 1

  4. Equation: 1 = m 3 3 1 Exploring the m • What is the slope?

  5. Equation: Equation: 2 = m 3 3 3 2 1 Exploring the m • What is the slope? What do you notice?

  6. 3 1 2 6 -4 m m m m m = = = = = 2 4 2 4 5 4 -4 5 6 2 -4 3 1 y y y = = = x x x 5 2 2 Calculate the slope for each line • What is the equation? 4

  7. What does the m represent? • The m represents the slope of the line. • Describes how steep the line is • The numerator tells us to go up or down (RISE) • The denominator tells us to go RIGHT (RUN) • If the numerator is positive we go up • If the numerator is negative we go down • Tells you the pattern in a table of values

  8. What is the slope and what does the m represent?

  9. Exploring the b • Look at the table and look at the equation. • What do you notice? • When x = 0 → y = 8 • Equation has + 8 Equation → y = 2x + 8

  10. Exploring the b • Look at the table and look at the equation. • What do you notice? • When x = 0 → y = 1 • Equation has + 1 Equation → y = -3x + 1

  11. 1 = m 2 2 2 2 2 1 1 1 1 Exploring the b • What is the slope? y = ½ x + 5 y = ½ x + 2 y = ½ x • What is the equation? • How do we tell them apart? y = ½ x - 3

  12. What does the b represent? • It is the y-intercept (where it crosses the y axis) • The value when x = 0 • Note: similar to sports, to intercept means to cross the pathway of the ball

  13. What does the equation tell you? • y = 4x - 1 • y = 3/2x + 2 • y = 1/5x - 3 • y = -2x • y = -5/2x + 10

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