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**In slope y-intercept form (y = mx +b)**

6.1 The Equation of a Line In slope y-intercept form (y = mx +b) Quick Review! Identifying slope and y-intercept from a graph Graphing a line given m and b Interpreting linear relations

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**Identifying Slope and y-intercept**

Identify the slope and y-intercept of this line, then use these values to create the equation of the line. m = 2/3 b = - 5 y = (2/3)x- 5

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**Special Lines! (Horizontal)**

Identify the slope and y-intercept of this line, then use these values to create the equation of the line. m = - 3 b = y = - 3

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**Special Lines! (Vertical)**

What is the slope (m) of a vertical line? The equation of this line is x = 7 The slope is undefined. What is the y-intercept (b) of this vertical line? There is no y-intercept. This means that for any point on this line, x is always 7, no matter what the y-coordinate is. A vertical line cannot be expressed in the form y = mx + b

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Let's Recap! x-intercept: the x-coordinate of the point where a line crosses the x-axis. At this point, y = 0. y-intercept: the y-coordinate of the point where a line crosses the y-axis. At this point, x = 0.

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**Graphing a Line given m and b**

Step 1: Plot the y-intercept first Step 2: Use the slope to find another point on the line, then connect the points. Graph the line with a slope of -4 and a y-intercept of 5 m = -4/1 b = 5 What is the equation of this line? Y = -4x + 5

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**Interpreting Linear Relations**

Identify the slope and vertical intercept of each of the following linear relations and explain what they mean. Write an equation to describe the relationship.

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**Interpreting Linear Relations**

b = 25 m = 5 The vertical intercept represents the initial cost of the tennis club membership. The tennis club charges an initial, upfront fee of $25. y = 5x + 25 The slope represents the cost to play tennis per day. Thus, it costs an additional $5 per day to play tennis at this club.

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**Interpreting Linear Relations**

b = 10 m = 5 The vertical intercept represents the initial cost of the movie membership. The membership has an initial flat fee of $10. y = 5x + 10 The slope represents the cost per movie rented. Thus, it costs an additional $5 per movie rented.

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**Interpreting Linear Relations**

b = 10 m = -1 The vertical intercept represents the initial height of the kite. The kite begins at 10m above the ground. y = -x + 10 The slope represents the rate at which the kite descends to the ground. It is descending at 1 meter per second, or 1 m/s

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Time to Practice!

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