Question

The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:

Part A: Find and interpret the slope of the function. (3 points)

Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)

Part C: Write the equation of the line using function notation. (2 points)

Part D: What is the balance in the bank account after 5 days? (2 points)

Answer 1

answer:

Explanation:
part a:
y2 - y1 / x2 - x1 = m
(2, 1350) (4, 1200)
(x1, y1) (x2, y2)
1200 - 1350 / 4 - 2 = m
-150 / 2 = m
-75 = m
part b:
y - y1 = m(x - x1)
y - 1350 = -75(x - 2)
y = mx + b
y = -75x + 1500
ax + by = c
y = -75x + 1500
+75 +75
75y = x + 1500
- x -x
75y - x = 1500
part c:
f(x) = -75x + 1500
part d:
f(5) = -75(5) + 1500
f(5) = -375 + 1500
f(5) = 1125

Answer 2

see below

Explanation:

Part A

The slope is found by

m = ( y2-y1)/(x2-x1)

= ( 1200-1500)/(4-0)

= -300/4

=-75

Part B

point slope y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y-1200 = -75(x-4)

slope intercept y = mx+b where m is the slope and b is the y intercept

y = -75x + 1500

standard form Ax+By =C

75x + y = 1500

Part C

Change y to g(x) in the slope intercept form

g(x) = -75x + 1500

Part D

Let x = 5

g(5) = -75(5) + 1500

=-375+1500

=1125