a)
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for calcualting slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of selected initial and final points on the line.
x1 and x2 are the x coordinates of the selected initial and final points on the line.
Considering the points on the line, we have
x1 = 0, y1 = 120
x2 = 2, y2 = 0
By substituting these values into the formula,
m = (0 - 120)/(2 - 0) = - 120/2
m = - 60
The y intercept is the value of y at the point where the line touches the y axis. From the graph, y intercept = 120
Thus,
Slope = - 60
y intercept = 120
b) By substituting these values into the slope intercept equation, the equation of the line is
y = - 60x + 120
c) From the graph, at time, x = 2 hours, the number of cups of lemonade, y = 0. If the game lasts for 2.5 hours, the amount of time left in the game when the student runs out of caups of lemonade is
2.5 - 2 = 0.5
The time left is 0.5 hour