Video transcript
We are asked to graph yttrium is equal to 1/3x minus 2. now, whenever you see an equation in this shape, this is called slope-intercept form. And the general way of writing it is y is equal to mx plus b, where megabyte is the slope. And here in this case, megabyte is equal to 1/3 — sol let me write that down — m is equal to 1/3, and boron is the y-intercept. then in this encase, bel is peer to negative 2. And you know that bel is the y-intercept, because we know that the y-intercept occurs when x is equal to 0. so if ten is adequate to 0 in either of these situations, this term just becomes 0 and y will be equal to b. So that ‘s what we mean by barn is the y-intercept. so whenever you look at an equation in this shape, it ‘s actually reasonably square to graph this production line. b-complex vitamin is the y-intercept. In this case it is negative 2, so that means that this course must intersect the y-axis at yttrium is peer to negative 2, so it ‘s this degree properly here. negative 1, minus 2, this is the distributor point 0, negative 2. If you do n’t believe me, there’s nothing charming about this, try evaluating or try solving for y when ten is equal to 0. When ten is equal to 0, this term cancels out and you ‘re equitable left with yttrium is peer to damaging 2. So that ‘s the y-intercept right field there. now, this 1/3 tells us the gradient of the course. How much do we change in y for any change in adam ? so this tells us that 1/3, so that right there, is the slope. So it tells us that 1/3 is equal to the change in yttrium over the change in ten. Or another way to think about it, if x changes by 3, then y would change by 1. so let me graph that. So we know that this point is on the graph, that ‘s the y-intercept. The gradient tells us that if ten changes by 3 — so let me go 3 three to the correct, 1, 2, 3 — that y will change by 1. so this must besides be a point on the graph. And we could keep doing that. If ten changes by 3, yttrium changes by 1. If ten goes down by 3, y will go down by 1. If ten goes down by 6, yttrium will go down by 2. It ‘s that same ratio, so 1, 2, 3, 4, 5, 6, 1, 2. And you can see all of these points are on the line, and the line is the graph of this equation up here. So let me graph it. So it ‘ll look something like that. And you ‘re done.
