y = mx + b What does the m and b represent?

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Presentation transcript:

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

Exploring the m Equation → y = 2x + 8 We already know that in a table of values for a linear relationship a pattern will form. This pattern is the rate of change. X Y -2 4 -1 6 8 1 10 2 12 Pattern → up by 2 Equation → y = 2x + 8

Exploring the m Equation → y = -3x + 1 What is the pattern? X Y -2 7 -1 4 1 2 -5 Pattern → down by 3 What is the equation? Equation → y = -3x + 1

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

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

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

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

What is the slope and what does the m represent?

Exploring the b Equation → y = 2x + 8 Look at the table and look at the equation. What do you notice? X Y -2 4 -1 6 8 1 10 2 12 When x = 0 → y = 8 Equation has + 8 Equation → y = 2x + 8

Exploring the b Equation → y = -3x + 1 Look at the table and look at the equation. What do you notice? X Y -2 7 -1 4 1 2 -5 When x = 0 → y = 1 Equation has + 1 Equation → y = -3x + 1

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

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

What does the equation tell you? C = 5h + 20 The rate of change is 5 (slope) and the initial value is 20 (y-intercept) y = -2x The slope is -2 and the line starts at (0,0) y = -5/2x + 10 The slope is -5/2 and the y-intercept is the same