Answer: y = 12x + 50
Step-by-step explanation:
Let y represent the cost of having the party.
Let x represent the number of people who would attend the party.
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the information given
y2 = 590
y1 = 290
x2 = 45
x1 = 20
Slope,m = (590 - 290)/(45 - 20) = 300/25 = 12
To determine the intercept, we would substitute x = 20, y = 290 and m= 12 into y = mx + c. It becomes
290 = 12 × 20 + c = 240 + c
c = 290 - 240 = 50
The equation becomes
y = 12x + 50
