Presentation on theme: "In slope y-intercept form (y = mx +b)"— Presentation transcript:
1In 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
2Identifying 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
3Special 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
4Special 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
5Let'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.
6Graphing 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
7Interpreting 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.
8Interpreting 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.
9Interpreting 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.
10Interpreting 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