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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 1: Heart of algebra- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example
- Linear equation word problems — Basic example
- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example
- Systems of linear equations word problems — Basic example
- Systems of linear equations word problems — Harder example

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# Graphing linear equations — Harder example

Watch Sal work through a harder Graphing linear equations problem.

## Want to join the conversation?

- The practices have no relation to these examples. So how do I do the practices?(31 votes)
- For me, all the practice questions had to do with finding the slope of the line. Assuming you had the same questions as I did, just count how many blocks you have to the next point on your y axis (going up). That number would be your numerator. Then count how many blocks along your x axis (going across) you have between your points and that will be your denominator. Your points are wherever your line goes right across the corner of a block. That's just how i learned it at least.(10 votes)

- why is the video cut short?(18 votes)
- This is a fault with Khan Academy. When Sal recorded this video, he must have accidentally stopped the recording. If you wish to ask Khan to fix it, go to Khan Zendesk: https://khanacademy.zendesk.com/hc/en-us/sections/205898887-General-Site-Networking and file a complaint.(8 votes)

**Hello**Test takers you've got this!!(18 votes)- Its not showing the full video(11 votes)
- I understand how you got the answer, but shouldn't D be correct as well? If x=0 and y=1, it would give you -6=-6. Could someone clear this out for me? Thank you!(6 votes)
- Nasim Mahdi, The eqaution should satisfy both points, i.e. (0,1) and (6,1).

The last equation doesn't satisfy the equation.

So, second choice is only the correct choice.

I hope you are clear.(6 votes)

- why we multiply -3 in the end? i didn't get that(5 votes)
- We multiply by -3 because -3 is the slope that we found our line to have. The last step of the problem is for us to plug in our equation for g (the second line) for the point -2. The equation of a line is y = mx + b, where m is the slope, b is the y-intercept, and x and y is a coordinate on the graph. We multiply by the slope simply because we have x and want to get to y, so we should multiply by m and add b to get y. Does that make it clearer?(7 votes)

- around2:25, with the fraction 1/6x .. why is it that he multiplied 6 to both sides instead of 1/6 ? i understand the key is to get x alone , so basically its 1x/6 ?(8 votes)
- how many methods are there for solving a quadratic equation apart from the following:

1. factoring method

2. middle term splitting

3. quadratic formula

4. completing the square method

5. graphing quadratic equation

also is the Factoring method and splitting the middle term method is same or not?(6 votes) - The video doesn't play over 32seconds for me either. :( Eh.(6 votes)
- How did he know that he had to replace y with g(x) in slope intercept form (y=mx+b)? Is this what you need to do in similar problems with g(x)?(4 votes)
- Because y is the same thing as the function of something. So, y is the same as anything of x. So, f(x), g(x), s(x), p(x), etc.

Hope this helps!(2 votes)

## Video transcript

- [Instructor] We're told the
graph of the linear function f is shown in the xy plane
above, we see that there. The graph of the linear
function g, not shown, is perpendicular to the graph of f and passes through the point 1,-5. What is the value of g of -2? Pause this video and see if you can work through this before we do this together. All right, now, one technique we can do is just try to figure
out the equation of g. So, we're going to have g of
x is going to be in the form the slope times x plus the y intercept. So, first of all, let's think about what the slope is going to be. And if g is perpendicular to f that means that g's slope is going to be the negative reciprocal of f's slope. So, what is f's slope? Well, it looks like for every three we move to the right we move up one. Every three we move to
the right we move up one. Or when the change in x is equal to three the change in y is equal to one. We know that slope is change
in y over change in x. So here, the slope is one third. Let me write that down. If we were actually taking the SAT you wouldn't write it down, take the time. But we might as well, over here. Slope is equal to one third,
so what's m going to be for g? Well, it's going to be the
negative reciprocal of that. So, we could say g of x is going to be the negative reciprocal of 1 over 3 is -3 over 1, or just -3x plus b. Now, we need to figure
out b well, luckily, they give us a point over here, 1, -5. So, we know that when x is equal to 1, so -3 times 1 plus b, then g of 1 is -5. So, this is going to be equal to -5. And so, we can solve for b,
-5 is equal to -3 plus b. And so, we can add -3 to both... or sorry, we could add 3 to both sides, and we are going to get -2 is equal to b. Add 3 to both sides, this
cancels, and then you get -2. And so, now, we know the equation for g. g of x is equal to -3x minus 2. And now we just go back
and say, all right then, that means g of -2 is going
to be -3 times -2 minus 2. Well, that is 6 minus
2, which is equal to 4. And we are done. Now, there's other ways that
you could approach this. You could say if the slope of g is -3 and if we start at 1, -5 and
we're trying to get to -2 let me write it this way,
if we have x and g of x, and we know when x is 1, g of x is -5, and we want to figure out what
about when x is equal to -2, well to go from 1 to -2,
you need to subtract 3. So if the slope is -3
that means on this side, right over here, -3 times -3
you're going to have to add 9. And so, -5 plus 9 is 4, that's another way that you could have approached this.