Writing equations of perpendicular lines | Analytic geometry (video) | Khan Academy

Video transcript

We ‘re asked what is the equality of telephone line B ? And they tell us that line A has an equation yttrium is equal to 2x plus 11. And they say that the line B contains the point 6, veto 7. And they tell us lines A and B are perpendicular, so that means that slope of B must be minus inverse of gradient of A. so what we ‘ll do is figure out the slope of A, then take the negative inverse of it. then we ‘ll know the slope of B, then we can use this point right here to fill in the gaps and name out B ‘s y-intercept. So what ‘s the slope of A ? This is already in slope-intercept form. The slope of A is right there, it ‘s the 2, maxwell plus b. So the gradient here is equal to 2. So the slope of A is 2. What is the gradient of B ? So what is B ‘s slope going to have to be ? Well, it ‘s perpendicular to A, so it ‘s going to be the minus inverse of this. The inverse of two is 1/2. The negative inverse of that is negative 1/2. So B ‘s slope is negative 1/2. So we know that B ‘s equation has to be y is equal to its slope, m times ten plus some y-intercept. We inactive do n’t know what the y-intercept of B is, but we can use this data to figure it out. We know that yttrium is equal to negative 7 when ten is equal to 6. negative 1/2 times 6 plus barn, good ? I good know that this is on the point, so this point must satisfy the equation of line B. So lashkar-e-taiba ‘s work out what boron must be — or what b, the y-intercept, this is a small letter bacillus, not the tune B. So we have negative 7 is equal to — what ‘s veto 1/2 one-half times 6 ? That ‘s not a barn there, that ‘s a 6. What ‘s negative 1/2 times 6 ? It ‘s negative 3, is adequate to negative 3 plus our y-intercept. Let ‘s add 3 to both sides of this equality, thus if we add 3 to both sides — I equitable want to get rid of this 3 properly here — what do we get ? The left side, negative 7 plus 3 is negative 4, and that ‘s going to be equal to — these guys cancel out — that ‘s equal to b, our y-intercept. So this right hera is a veto 4. So the equality of wrinkle B is yttrium is equal to — its slope is a negative inverse of this character — so negative 1/2, negative 1/2 ten. And its y-intercept we just figured out is negative 4. And we are done.

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