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### Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 2: Topic B: Linear equations in two variables and their graphs- Rates & proportional relationships example
- Rates & proportional relationships: gas mileage
- Rates & proportional relationships
- Graphing proportional relationships: unit rate
- Graphing proportional relationships from a table
- Graphing proportional relationships from an equation
- Graphing proportional relationships
- Points on the coordinate plane examples
- Testing solutions to linear equations
- Solutions to 2-variable equations
- Graphing a linear equation: 5x+2y=20
- Complete solutions to 2-variable equations

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# Testing solutions to linear equations

Sal figures out which equation was used to generate a table of x and y values. Created by Sal Khan.

## Want to join the conversation?

- In one of the exercises, they have f(x) at the top of a column. Is that one variable?(6 votes)
- If I am given a table of ordered pairs for a line, how do I determine what the equation is for the table of values given?

(2, -3) , (4, -2), (6, -1) , (7, -0.5)(6 votes)- You know if the line isn't vertical that the equation for it will be y = m.x + b.

In this equation, m will be the slope and can be calculated the following way:

m = (a - c)/(d - e), if points (d,a) and (e,c) belong to the line.

b is the point where the line intersects the yy axis, but you can figure it out by finding m and then substituting x and y by a point.

Ex: if we take points (2,-3) and (4,-2), then:

m = [-3 -(-2)]/[2-4] = -1/(-2) = 1/2

If we substitute x and y by the point (2,-3):

-3 = 1/2*(2) + b <=> b = -3 - 1/2(2) = -3-1 = -4

Therefore the equation for the line is: y = 1/2x - 4(2 votes)

- find the table for linear equations y=-4x-1(3 votes)
- x=-1/4 where y=0

and y=-1 where x=0

The co ordinates are,therefore, (-1/4,0) and (0,-1)(1 vote)

- My teache gave me a proble were x=2 and we have to graph and create a table how can i do that?(2 votes)
- Think of a situation in which x is always 2, no matter what y is.

When y = 0, x = 2. When y = 1, x = 2.(2 votes)

- How would you find the linear equation to the ordered pairs if you did NOT have a selection of equations for you?(2 votes)
- If you have at least two points, you can find the equation of the line that goes through them. Is that what you are trying to find?

Use the two points and calculate the slope between them (difference between the y coordinates)/(difference between the x coordinates).

Then you can fill it in for 'm' in a slope-intercept form equation template:

y = mx+b

After you do that (say, like if you get 3 for the slope) you would have

y = 3x+b.

Then use either one of the points you have and fill in the x and the y into the equation. Then the only variable in the equation would be 'b' and you could solve for it.

So then you'd have the slope (m) and the y-intercept (b). and you'd have allt he information you need to write the equation for the line between the two points. y=mx+b(2 votes)

- (-7,-8) and (-4,-1) how to find linear equation(2 votes)
- Is there any probability you could do college level algebra videos?(1 vote)
- He did linear algrebra, I don't know if that's what you mean but yea.(1 vote)

- i cant understand the point of haveing the x value and its like x is 4 x is 7 which one is it exzatilay and i can under stand the whole thing with negitives(1 vote)
- Here's an example: 5x. 5 is the coefficient. x is the variable. The coefficient of x can be any nonzero number, including negatives. If x=5, then we plug in for x. 5x → 5 times 5. The answer is 25.

Hope this helps and have a great holiday!(1 vote)

- gaur bought 2 kinds of cloth materials. he bought shirt material for 50 dollar per metre and skirt for 90 dollar per metre. for every two metres of the trouser material he bought 3 metres of skirt material. he sells the materials at 12% and 10% profit respectively. his total sale is 36660 dollars. how much trouser material did he buy ?(1 vote)
- how can i solve y=5x - 3(1 vote)

## Video transcript

Some ordered pairs
for a linear function of x are given in
the table below. Which equation was used
to generate this table? So they give us a
bunch of data points. When x is 4, y is negative 8. When x is 7, y is negative
20, so on and so forth. And these points
have been generated by one of these equations
right over here, so let's just see which
of these equations actually could have generated
all of these points. So let's go to this first
point right over here, 4 comma negative 8, and let's
go equation by equation. If x is 4 here, negative 2
times 4 would be negative 8. Let me just write it down. We'd multiply negative 2
times 4 to get negative 8, and then I would add
1 to get negative 7. I would get negative 7. So for this equation,
when x is 4, y would be negative
7, not negative 8. So this equation
definitely did not generate this top
point right over here. So we could just rule it out. Whatever equation
should have been able to generate
for any given x, for any of these x's, should
generate this y right over here. Now let's go to
this next equation. y is equal to
negative 2x plus 0. So when x is 4, y would
be negative 2 times 4, which is negative 8. So this second
equation seems to be capable of generating
this first set of points. When x is 4, y is negative 8. But let's see if it
works for this second one right over here. When x is 7, you
would have negative 2 times 7, which is negative
14, but here, when x is 7, y is negative 20. So this one, we can rule
out, because when x is 7, y does not equal negative
20 like this point right over here. So we'll rule that
second one out. Now let's look at
this third one. y is equal to
negative 4x plus 8. Well, we could go to
this first point again. When x is 4, let's think about
what happens when x is 4. So when x is 4,
you have negative 4 times 4, which is negative 16,
plus 8, which is negative 8. So it seems to be able to
generate this first point. When x is 4, y is negative 8 for
this equation right over here. Now let's see what
happens when x is 7. So negative 4 times
7 is negative 28. Negative 28 plus
8 is negative 20, so this candidate is
starting to look pretty good. It's pretty good. It satisfies these two
points, and frankly, for any of these linear
functions, if it satisfies any of these two points, if some
linear function generated all of these, if some function
can generate any two of them, it will satisfy all of these,
because two points define a line. But we can verify
it right over here. So let's see what
happens when x equals 8. Negative 4 times 8 is negative
32, plus 8 is negative 24. So that satisfies so that when x
is 8, y does equal negative 24. And then finally, let's
look at that last point. When x is 9, negative 4
times 9 is negative 36, plus 8 is equal to negative 28. And that's exactly what
we see here in this table. So we don't even have
to look any further. Choice 3 satisfies
the conditions that when x is any
one of these things, the corresponding y that's
defined by this equation is going to be when x
is 4, y is negative 8. When x is 7, y is negative
20, so on and so forth.