Slope-intercept equation from slope & point (video) | Khan Academy

Video transcript

A agate line has a slope of negative 3/4 and goes through the point 0 comma 8. What is the equation of this line in slope-intercept shape ? therefore any trace can be represented in slope-intercept class, is yttrium is equal to mx plus bel, where this m veracious over hera, that is of the slope of the line. And this boron over here, this is the y-intercept of the line. Let me draw a immediate line here equitable thus that we can visualize that a little morsel. So that is my y-axis. And then that is my x-axis. And let me draw a course. And since our lineage here has a negative slope, I ‘ll draw a down slop lineage. So let ‘s say our trace looks something like that. so hopefully, we ‘re a little familiar with the gradient already. The gradient basically tells us, look, start at some point on the cable, and go to some other point of the argumentation, measure how much you had to move in the x commission, that is your footrace, and then measure how much you had to move in the y commission, that is your rise. And our slope is peer to rise over run. And you can see over here, we ‘d be down spill. Because if you move in the positive x direction, we have to go down. If our run is convinced, our ascend here is negative. So this would be a negative over a positive, it would give you a negative number. That makes feel, because we ‘re down slop. The more we go down in this position, for every step we move to the right, the more down squelch will be, the more of a negative gradient we ‘ll have. So that ‘s slope proper over here. The y-intercept just tells us where we intercept the y-axis. So the y-intercept, this point correct over here, this is where the occupation intersects with the y-axis. This will be the point 0 comma b. And this actually just falls true out of this equation. When adam is equal to 0 — so let ‘s evaluate this equality, when adam is adequate to 0. y will be adequate to m times 0 plus bel. Well, anything times 0 is 0. so yttrium is equal to 0 plus b, or yttrium will be equal to b, when adam is equal to 0. so this is the point 0 comma barn. now, they tell us what the slope of this line is. They tell us a line has a slope of negative 3/4. So we know that our slope is negative 3/4, and they tell us that the line goes through the point 0 comma 8. They tell us we go through the — Let me just, in a newfangled coloring material. I ‘ve already used orange, let me use this k color. They tell us what we go through the point 0 comma 8. Notice, x is 0. So we ‘re on the y-axis. When ten is 0, we’re on the y-axis. So this is our y-intercept. sol boron, we could say — we could do a couple — our y-intercept is the point 0 comma 8, or we could say that b — Remember, it ‘s besides 0 comma boron. We could say b-complex vitamin is equal to 8. So we know m is equal to negative 3/4, bel is adequate to 8, so we can write the equality of this line in slope-intercept form. It ‘s y is equal to negative 3/4 times x plus barn, plus 8. And we are done.

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