For the following exercises, write the equation of the line satisfying the given conditions in s

For the following exercises, write the equation of the line...

Key Concepts

y-Intercept

The y-intercept is the point where the line crosses the y-axis, where the value of x is zero. In the slope-intercept form, this value is directly represented by b. It is a key reference point in the graph of the line, helping to determine its position.

Slope Calculation

The slope of a line represents its steepness and direction. When two points on the line are known, including intercepts, the slope can be calculated using the formula (change in y)/(change in x). This calculated slope is essential for writing the linear equation in slope-intercept form.

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is particularly useful for graphing because it directly shows where the line crosses the y-axis and how steep the line is.

x-Intercept

The x-intercept is the point where the line crosses the x-axis. At this point, the value of y is zero. Knowing the x-intercept provides a specific point on the line that can be used along with other points to determine the line's slope or to establish its equation.

Transcript

00:01 Hey everyone, today we're solving problem number 74 from chapter 1, section 2 of the textbook, which asks us to write the equation in slope intercept form, given that our x intercept is equal to negative 6 and your y intercept is equal to 9.

00:15 So i'm going to just write out the generic equation for slope intercept form, which is that y equals mx plus b, where m is your slope and b is your y intercept value.

00:29 What's really great about this problem is that you can approach it a few different ways.

00:33 I'm just going to make sure that i have mx plus my y intercept value because that's already given to me, right? because that's the second piece of information given right here.

00:43 We're already told what our v value is.

00:45 We have plus 9.

00:49 So i'm just going to rewrite that.

00:51 We have y equals, sorry, mx plus 9, which i meant to write over here.

01:09 Again, that's your second piece of information given.

01:15 So we have mx plus 9.

01:17 All right, now knowing that, we're going to have to somehow use our first piece of information.

01:21 And the first piece of information is that your x intercept is negative 6.

01:25 All right, so how do we deal with that? well, an x intercept and a y intercept, in fact, are both actual coordinates on a linear function graph.

01:37 So the x intercept coordinate is when you have some value of x, which they give you in this case, negative 6, and y is always equal to 0.

01:46 Conversely, your y intercept is when your x value equals zero, and you have some sort of y value.

01:53 In this particular case, it's not.

01:56 So here are a few different ways you can approach this.

01:59 Number one, you can simply just use this and plug it into this equation to find what your slope is.

02:04 Or number two, you can use both of these coordinates and do the change in y or the change in x.

02:09 But to me, it's much simpler to just plug in this x intercept value coordinate, sorry, into what we have right now, because, we already have our y intercept value.

02:19 So when i plug it in, i have, let me write that in, actually...

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