Find an equation of the line that passes through the given point and is perpendicular to the giv

Find an equation of the line that passes through the given...

Key Concepts

Slope-Intercept Form

This is a way of expressing a linear equation as y = mx + b, where m is the slope and b is the y-intercept. It directly shows how steep the line is and where it crosses the y?axis, making it easy to graph and interpret the line.

Point-Slope Form

This form of a linear equation is useful when you have a known point (x?, y?) through which the line passes and the slope m. The formula is written as y - y? = m(x - x?), and it can be manipulated into other forms such as the slope-intercept form.

Perpendicular Lines

In coordinate geometry, two lines are perpendicular if the product of their slopes is –1. This means the slope of one line is the negative reciprocal of the other’s. This concept is critical when finding a line that is perpendicular to a given line.

Converting Linear Equations

Often, a linear equation might not be presented in slope-intercept form. Converting the equation into this form by isolating y helps identify the slope and y-intercept, which are essential in analyzing properties of the line such as its steepness and direction.

Transcript

00:01 So our goal on this example is to write the equation in slope intercept form that passes to the given point and is perpendicular to the given line.

00:09 So that's my blue line.

00:10 I've used two different colors on purpose to really show that there are two different lines happening.

00:17 Ultimately, my goal is to do slope intercept form that passes to the given point.

00:21 So that's red.

00:23 So if i could set up my answer right now, it would be down here and it would be all in red.

00:27 Y equals mx plus b and that's slope intercept form.

00:30 Now to have a slope intercept equation, i need a slope and a y intercept.

00:35 Here's my red information, and that's not a slope or a y intercept.

00:38 It's an x and a y coordinate.

00:40 But i am told that it's perpendicular to my given line.

00:45 So that's my blue line.

00:47 The reason that's important to know that they're perpendicular is because perpendicular lines have a special relationship with their slopes.

00:53 Their slopes are opposites and reciprocals.

00:56 So if i know the slope of my blue line, then i would be able to figure out the slope of my red line.

01:03 So let's see if i can find the slope of my blue line.

01:05 To look at an equation and know its slope right away, y should be isolated.

01:09 It should be in slope intercept form, because then once y is isolated, your slope is your coefficient of x.

01:14 In this case, y is not isolated.

01:16 So i'm going to go ahead and do that.

01:17 So to do that, i would add 8.

01:19 Then i have to do on the other side...

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