Write the equation of the line that passes through the points (1, 7) and (5, 15) using function notation. a) y = 2x + 5 b) y = 4x + 8 c) f(x) = 2x + 5 d) f(x) = 4x + 8

c) f(x) = 2x + 5

Step-by-step explanation:

slope  = (y2-y1)/ (x2-x1)

 m = (15-7)/(5-1)

  m = 8/4

m=2

point slope form for an equation is

y-y1 = m(x-x1)

y-7 = 2 (x-1)

distribute

y-7 = 2x-2

add 7 to each side

y-7+7 = 2x-2+7

y = 2x +5

it asks for the equation in function notation

f(x) = 2x+5

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

there are infinitely many solutions.