Question

Which function below has the lowest y-intercept?


f(x)

graph going through (0,5) and (4, 3)
g(x)

Kyle started the summer having read 3 books but plans to read 6 books per month over the summer.

h(x)

h(x) = 3x + 4

f(x)

g(x)

h(x)

The functions all have the same y-intercept.

Answer 1

Help please :c

Answer 2

We know that linear equations have a slope (m) and y-intercept (b): y=mx+b, where x and y are variables. One point for f(x) is <0,5>, where x=0 and y=5. Another point is <4,3>. So we have two equations and two unknowns. We then can solve for m and b:
$$
5=m(0)+b\\
4=m(4)+b
$$
Using the 1st equation, we immediately see that b=5. This is the y=intercept for f(x).

Make sense?

Answer 3

Okay, so then I would do 6 = m(3) + b for g(x)?

Answer 4

The second equation should have been
$$
4=m(3)+b
$$

Answer 5

Good guess. But saying that she "started" the summer reading 3 books, means that at x=0, y=3, using our equation notation: 3=m(0) + b. This immediately shows the y-intercept for g(x).

Answer 6

b = 3 ?

Answer 7

for g(x)

Answer 8

yes

Answer 9

Okay, just one more question. How would I find h(x)?

Answer 10

So you are given h(x): y=3x+5. Here m=3 and b=5. So you are essentially just given the y-intercept, b.

Collect all these y-intercepts and find the lowest one.
y-intercepts:
f(x) has b=?
g(x) has b=?
h(x) has b=?

Answer 11

So g(x) should be the answer correct?

Answer 12

note that h(x) just means " A function, let's call it 'h' and it is a function of 'x' " So, h(x)=y=3x+4.

Answer 13

Why?

Answer 14

I'm doing this for homework and just confused by this all

Answer 15

do you understand what we did here?

Answer 16

Yeah I do, the graph was obvious to me but the other two I was confused about

Answer 17

that's ok. Sometimes you need to see the problem in different ways to see that it really is all the same thing. In this case, everything boils down to y=mx+b, which is just a graph, with slope=m and that crosses the y-axis at y=b, when x=0.

Answer 18

Okay, I think I got it, thanks for your time! :)

Answer 19

No problem. Hope you start to enjoy math, it can be really fun.