Recall the slope-intercept form of a linear equation is given by the following formula:
y = mx + b ,
where 'm' is the slope of the line and 'b' is the y-intercept.
a) Given that it will cost $5 per person in addition to a charge of $100 just to reserve the rink, we can conclude that the total cost of the party is the $5/person fee multiplied by the # of people attending the party plus the $100 reservation fee. That is,
total cost of party = ($5/person)·(# of people attending) + ($100 reservation fee)
If we let 'y' represent the total cost of the party and 'x' represent the # of people attending the party, then
y = 5x + 100
b) Give the slope-intercept form of a linear equation: y = mx + b
And the equation we found to represent the total cost of the party: y = 5x + 100
The slope (m) is equal to 5 ==> $5/person OR 5 dollars/person
c) Graphically, the y-intercept (b) is the point where the line intercepts with the y-axis (algebraically, the y-intercept is the point on the line when x = 0).
Thus, if you graph the line y = 5x + 100 , the point at which the line crosses the y-axis is the y-intercept. When the line crosses the y-axis, the x-coordinate is thus 0. To find the y-intercept algebraically, plug in x=0 into the equation of the line:
y = mx + b ==> y = m(0) + b ==> y = 0 + b ==> y = b
y = 5x + 100 ==> y = 5(0) + 100 ==> y = 0 + 100 ==> y = 100