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## 8th grade

### Course: 8th grade > Unit 3

Lesson 10: Comparing linear functions- Comparing linear functions: equation vs. graph
- Comparing linear functions: same rate of change
- Comparing linear functions: faster rate of change
- Compare linear functions
- Comparing linear functions word problem: climb
- Comparing linear functions word problem: walk
- Comparing linear functions word problem: work
- Comparing linear functions word problems

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# Comparing linear functions: equation vs. graph

CCSS.Math: ,

Sal is given the formula of a linear function and the graph of another, and is asked to determine which function increases faster. Created by Sal Khan.

## Want to join the conversation?

- If ax + by + c = 0 is a linear equation in two variables. Is x + 0y + 7 = 0 a linear equation in 2 variables?(17 votes)
- Yes, the second example is also a linear equation in two variables. Similarly,
`0x + 0y + 0z = 0`

is a linear equation in three variables, albeit one with an infinite number of solutions.

Having a coefficient of 0 doesn't mean that the variable goes away. It still exists, it is simply irrelevant and can take on any value without affecting the validity of the equation.(9 votes)

- At0:30, how did Sal plot a "g" out of nowhere?(8 votes)
- He wasn't plotting a point named "g". He was showing that the line on the graph is the function "g(x)"; this is stated in the text of the exercise.(12 votes)

- my teacher wants me to (sooner or later) describe a linear function. how should I do that?(4 votes)
- Zachary,

Lets break up the word. Linear means something that makes a line (pretty simple,) and a function is a set of coordinates or points on a graph that have only one x value to every y value. So basically, a linear function does not curve, but goes in a strait line on a graph. If it curves, this is called a non-linear function.

I hope this helped!(20 votes)

- is y=1/x - 7 a linear function(3 votes)
- No, it isn't. Anything that has the formula y=m/x + q is a hyperbola function.(8 votes)

- At2:12, if both are increasing then don't the negatives cancel out and become positive?(5 votes)
- You are comparing the slopes, not multiplying the slopes.

Both lines are negative, so both lines slant down from left to right. The slope of line F is decreasing faster because its slope is more negative than the slope of line G.

Hope this helps.(3 votes)

- Graph the linear function with the equation y=1/2x+3(4 votes)
- Your equation is in slope-intercept form already so graphing it is pretty easy.

Just looking at the equation, you can tell it crosses the y-axis at (0,3) so plot that point.

Now use the slope (1/2) to find another point. Your slope tells you to go up one and over to the right 2 to get to the next point. Since it's a positive number, your line will slope upwards.

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|f you aren't comfortable with the slop-intercept form yet, I suggest:

https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func/alg-slope-intercept-form/v/slope-intercept-form(4 votes)

- I dont understand where is line f. How do we know that it is decreasing? And when calculating the slope of f ,why is just -7/3x considered ,and not +1 (f = -7/3x + 1)(4 votes)
- f is only shown as an equation. Its slope is -7/3. The negative means that it is a downward slope. [-7/3 is a downward slope. 7/3 would be an upwards slope]. The slope of the line, g is -2/1. When calculating the slope we want to figure out the numbers before x

example: -7/3 x . The +1 is the point where the line crosses the y axis. It isn't used to calculate slope unless we are using it as one of two points to use the y2-y1 / x2-x1 process. We are not using this process because we already know the slope is -7/3.(2 votes)

- Why are both f and g both decreasing? Looking at the graph, I'm totally confused by this. In which direction is the line "moving"?(4 votes)
- The graph should be read from left to right, or in other words from low input (x-) values to high ones. The steeper the graph, the higher the increase or decrease.(1 vote)

- -7/3 = -7/3 = 7/-3 so how do you know whether it is 3 right 7 down or 7 up 3 left? In other words both are change in y over change in x so how do you know what the slope is if you are only given -7/3 = 7/-3?(3 votes)
- 3 right, 7 down is the same as 7 up, 3 left just like how -7/3=7/-3 so it doesn't actually matter. Usually, you'll see that the vertical direction (change in y) is first and right is always used for the horizontal direction (change in x), so in this case, 7 down, 3 right would be used.(1 vote)

- will i need to do this in grade 10?(2 votes)
- Yes, it is likely that you will need this skill in grade 10. In math, any skill you learn now is likely needed at some time in higher grade levels. This is because higher level math skills often depend on lower level math skills.

Have a blessed, wonderful day!(3 votes)

## Video transcript

Two functions, f and
g, are described below. Which of these statements
about f and g is true? So they defined
function f as kind of a traditional linear
equation right over here. And this right over here is g. So this right over
here is g of x. And that also looks
like a linear function. We see it's a kind of a
downward sloping line. So let's look at our choices
and see which of these are true. f and g are both increasing, and
f is increasing faster than g. Well, when I look at g--
Well, first of all, g is definitely decreasing. So we already know
that that's false. And f is also decreasing. We see here it has
a negative slope. Every time we move forward
3 in the x direction, we're going to move down 7
in the vertical direction. So neither of these
are increasing so that's definitely not right. f and g are both increasing. Well, that's
definitely not right. So we know that both f
and g are decreasing. So this first choice says
they're both decreasing, and g is decreasing faster than f. So let's see what
the slope on g is. So the slope on g is every time
we move 1 in the x direction, positive 1 in the
x direction, we move down 2 in the y direction. So for g of x, if we were
to write our change in y over our change in x-- which
is our slope-- our change in y over change in x, when we
move one in the x direction, positive 1 in the
x direction, we move down 2 in the y direction. So our change in y over
change in x is negative 2. So g has a slope of negative 2. f has a slope of negative 7/3. Negative 7/3 is the same
thing as negative 2 and 1/3. So f's slope is more negative. So it is decreasing faster. So g is not decreasing faster
than f. f is decreasing faster than g. So this is not right. And then we have this choice--
f and g are both decreasing, and f is decreasing
faster than g. This is right, right over here. We have this last choice-- g is
increasing but f is decreasing. We know that's not true.
g is actually decreasing.