Find the equation of the line using the point-slope formula. Write all the final equations using

Find the equation of the line using the point-slope formula....

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Key Concepts

Perpendicular Line Slopes

In the context of linear equations, two lines are perpendicular if the product of their slopes is -1. This means that the slope of one line is the negative reciprocal of the slope of the other, a key property used to determine the equation of one line from another.

Point-Slope Form

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a known point on the line. This form is particularly useful for writing the equation of a line when you know one point and the slope.

Slope-Intercept Form

This form of a linear equation is written as y = mx + b, where m represents the slope of the line and b its y-intercept. It is widely used for graphing and quickly identifying a line's steepness and where it crosses the y-axis.

Transcript

00:01 All right, so we need to find an equation perpendicular to this one that goes through this point right here, negative 2 comma 1.

00:08 And so the first thing we should notice right away is this is not in slope intercept form.

00:15 And so the way we do that is we multiply, and i'll just rewrite this, 3y is equal to x minus 4.

00:23 We need to multiply this, i'll do it in red, times a negative, a 1 third, because so we need to multiply this.

00:30 3 divided by 3 or 3 times a third is 1, leaving us with y.

00:35 And if i multiply this whole thing over here times a third, i can see that that 1 3rd is going to be a coefficient to the x right there.

00:48 And yeah, negative 4 times a 3rd is going to be negative 4 thirds also.

00:54 It doesn't really matter because all we care about is this 1 3rd.

00:58 Because the way to make an equation perpendicular is to look at the slope right here.

01:06 So to make it perpendicular, this one -third has to flip to the reciprocal, which is 3 over 1, or 3.

01:13 It also has to become negative.

01:15 So we immediately know our equation is going to be y equals negative 3x.

01:20 Now all we have to do is find b.

01:23 And we can find b by using this formula here.

01:26 So let's go ahead and plug in our y...

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