In the following exercises, find an equation of a line parallel to the given line and contains t

In the following exercises, find an equation of a line...

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Key Concepts

Using a Given Point in Line Equations

To define a specific line, one can use the known slope (from the property of parallelism) along with a point through which the line passes. Substituting the coordinates of this point into the line's equation allows one to solve for unknown parameters, such as the y-intercept.

Converting to Slope-Intercept Form

When a linear equation is provided in a different format, such as standard form, it is often converted to slope-intercept form by solving for y. This conversion clarifies the slope and intercept, facilitating further analysis and usage in problems involving parallel lines.

Slope-Intercept Form

This is a method of writing the equation of a line in the form y = mx + b, where m represents the slope and b represents the y-intercept. It makes it straightforward to identify and compare slopes and positions of lines.

Parallel Lines

Parallel lines share the same slope while having different y-intercepts. Recognizing that any line parallel to a given line must have an identical slope is a key property when formulating equations for parallel lines.

Transcript

00:01 Alright, this question wants us to give the equation of a line parallel to 2x plus 3y equals 6, 3 .05, and it wants us to write our equation in slope intercept form, which is y equals mx plus b.

00:12 It's currently in standard form.

00:16 So the first thing we're going to do is convert this equation to slope intercept form, and then it's really easy to see our slope that way.

00:22 So in order to do that, we need to get the y by itself.

00:24 So we're going to use our algebra tools to move this to the other side.

00:30 First, we always work our way toward the outside and then towards the y.

00:38 So whenever i subtract the 2x, i like to put it at the beginning, so my x term comes first.

00:45 And then to separate the 3 from the y will divide by 3.

00:50 So i have y equals negative 2 thirds x and then 6 divided by 3 is 2.

00:59 So if it's parallel to this equation we're going to be using the slope.

01:03 We do not need the b value at all.

01:08 We're going to have a new b value.

01:09 So our answer is going to look like this.