Question

The graphs of functions f(x) and g(x) = f(x) + k are shown below.

graph of line f of x going through ordered pairs 0, 1 and 2, 6. Graph of line g of x going through ordered pairs 0, negative 1 and 2, 4.

The value of k is ___.

Answer 1

So f(x) goes through (0,1) and (2,6)
g(x) goes through (0, -1), and (2,4), correct?

Answer 2

Yes

Answer 3

Find the equation of g(x) by first finding the slope, then using point slope form to find the equation.

Answer 4

Truth is I have no idea how to use point slope

Answer 5

Do you know how to find the slope of g(x)?

Answer 6

5/2 ?

Answer 7

@Embryo plz help

Answer 8

oh larry youre back!

Answer 9

(y2-y1)/(x2-x1) = (6-1)/(2-0) = 5/2

point slope form:

y-y1=m(x-x1)

choose a point, and solve for the equation. Lets use (2,6)

y1 = y coordinate
m = slope
x1 = x coordinate

Answer 10

You could also just look at the graph, and see what needs to be added to make f(x) = g(x)

Answer 11

-2?

Answer 12

@larryboxaplenty

Answer 13

y-(6)=(5/2)(x-2)
y-6=(5/2)x-5
+6 +6

y = (5/2)x +1
f(x) = (5/2)x+1

Answer 14

So the answer is f(x) = (5/2)x+1 ?

Answer 15

No, that's the equation for f(x), now do the same for g(x), and set it up as

f(x)+k = g(x), and solve

Answer 16

?

Answer 17

What is the slope for g(x) ?

(0, -1), (2,4)

(y2-y1)/(x2-x1)

m = (4-(-1))/(2-0) = 5/2

Pick a point lets use (2,4)

y-y1=m(x-x1)
y-4=(5/2)(x-2)
y-4=(5/2)x-5
+4 +4

y = (5/2x-1
g(x) = (5/2)x-1

Answer 18

f(x) = (5/2)x+1
g(x) = (5/2)x-1
--------------
g(x) = f(x)+k

(5/2)x-1 = (5/2)x+1+k

Answer 19

Do you see what k is?

Answer 20

k = -2?

Answer 21

Yes

Answer 22

Make sense?

Answer 23

Thak You and yes and btw that's what I put like a century ago lol

Answer 24

did you find the answer? @mathman 123