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2 votes
3. Sam and Tim each have savings accounts. Every month they each put in some of their

earnings from mowing lawns. Use the tables to find the y-value of the solution to the
system shown.
х
1
2
3
4
f(x)
80
110
140
170
х
1
2
3
4
g(x)
100
120
140
160

User JhTuppeny
by
4.8k points

1 Answer

2 votes

Answer:


y = 30x +50 --- Sam


y = 20x +80 --- Tim

Explanation:

Given

Sam Tim

х --- f(x) --------------- g(x)

1 --- 80 --------------- 100

2 --- 110 --------------- 120

3 --- 140 --------------- 140

4 --- 170 -------------- 160

Required

Determine the y value

y value implies the equation of the table

Calculating the equation of Sam

First, we need to take any corresponding values of x and y


(x_1,y_1) = (1,80)


(x_2,y_2) = (4,170)

Next, we calculate the slope (m)


m = (y_2 - y_1)/(x_2 - x_1)


m = (170 - 80)/(4 - 1)


m = (90)/(3)


m = 30

Next, we calculate the line equation using:


y - y_1=m(x-x_1)


y - 80 = 30(x - 1)


y - 80 = 30x - 30

Make y the subject


y = 30x - 30 + 80


y = 30x +50

Calculating the equation of Tim

First, we need to take any corresponding values of x and y


(x_1,y_1) = (1,100)


(x_2,y_2) = (4,160)

Next, we calculate the slope (m)


m = (y_2 - y_1)/(x_2 - x_1)


m = (160 - 100)/(4 - 1)


m = (60)/(3)


m = 20

Next, we calculate the line equation using:


y - y_1=m(x-x_1)


y - 100 = 20(x - 1)


y - 100 = 20x - 20

Make y the subject


y = 20x - 20+100


y = 20x +80

User Mickey Cohen
by
4.4k points