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

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Presentation transcript:

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

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

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

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

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.

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

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.

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.

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.

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

Time to Practice!