Presentation on theme: "In slope y-intercept form (y = mx +b)"— Presentation transcript:
1 In slope y-intercept form (y = mx +b) 6.1 The Equation of a LineIn slope y-intercept form (y = mx +b)Quick Review!Identifying slope and y-intercept from a graphGraphing a line given m and bInterpreting linear relations
2 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 =2/3b =- 5y = (2/3)x- 5
3 Special Lines! (Horizontal) Identify the slope and y-intercept of this line, then use these values to create the equation of the line.m =- 3b =y = - 3
4 Special Lines! (Vertical) What is the slope (m) of a vertical line?The equation of this line isx = 7The 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 formy = mx + b
5 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.
6 Graphing a Line given m and b Step 1: Plot the y-intercept firstStep 2: Use the slope to find another point on the line, then connect the points.Graph the line with a slope of -4 and ay-intercept of 5m = -4/1b = 5What is the equation of this line?Y = -4x + 5
7 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.
8 Interpreting Linear Relations b = 25m = 5The vertical intercept represents the initial cost of the tennis club membership. The tennis club charges an initial, upfront fee of $25.y = 5x + 25The slope represents the cost to play tennis per day. Thus, it costs an additional $5 per day to play tennis at this club.
9 Interpreting Linear Relations b = 10m = 5The vertical intercept represents the initial cost of the movie membership. The membership has an initial flat fee of $10.y = 5x + 10The slope represents the cost per movie rented. Thus, it costs an additional $5 per movie rented.
10 Interpreting Linear Relations b = 10m = -1The vertical intercept represents the initial height of the kite. The kite begins at 10m above the ground.y = -x + 10The slope represents the rate at which the kite descends to the ground. It is descending at 1 meter per second, or1 m/s