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## Heart of algebra

# Graphing linear equations — Harder example

## 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.