Answer:
That it's confusing to you is understandable, these problems are confusing, They take a bunch of real world things and put it into abstract concepts. The graph of the line is just that, an idea of how math represents the cost of the milk.
Step-by-step explanation:
the graph you are given is a straight line, not all graphs are straight lines, but b/c it's a straight line we get to "categorize" it as linear. linear graphs are nice to work with, as compared to curvey ones. aka non-linear. There are a few famous formulas that go along with linear graphs. Remember graphs are just representations of info in a way that we can use math to understand that real thing in abstract ways.
the problem asks what is the slope of the line. Think of the idea of a mountain slope here, when we look at the graph.. and move over it like we would read, from left to right, the graph moves up hill.. or positive, so this graph is a positive slope graph. now we just need to figure out a way to say that with numbers.
often times slope is represented with the variable 'm' . why 'm' you ask? it's just a convention, it's not important which letter you use to represent slope but by convention we use 'm' There is a formula for slope that goes like this,
m = (y2-y1) / (x2-x1)
we can use that to find the slope of this line, but we already know it's positive just by quickly looking at the graph.
the x's and y's in the formula are the x and y points of some exact point on the graph that we can find just by looking at the graph. :) yes we get to make our own points. P1 and P2 ( point 1 and point 2)
somebody has already made two nice black dots, on your graph for you, let's use those two black dots, you don't have to, but those do look convenient. :)
using those two black dots and going from left to right.. I see the 1st point as P1 = (x1,y1) =( 2,10) and the second point as P2 = (x2,y2) = (4,20)
then plug those into the above fomula
m = (20-10) / (4-2)
m = 10 / 2
m = 5
yep, it's positive and steep up , that the answer to (a)
for (b)
we just need the formula called the point slope
y = mx + b
since we know m
y = 5x + b
for use b = 0
so just
y = 5x
now plug in x= 1/2, for the 1/2 gallon of milk
y = 5(1/2)
y = 2/5
that's (b) :)
