Identify the 𝒚– intercept & slope of y=−2x−3y=-2x-3y=−2x−3 . Then graph the equation.

b=−3,m=−2b=-3,m=-2b=−3,m=−2

Identify the 𝒚– intercept & slope of y = − 2 x − 3 y=-2x-3 y = − 2 x − 3 . Then graph the equation .

Hey, everyone. Welcome back. So in this example, we're asked to identify the y intercept and slope of this equation that's given to us, negative 2x minus 3, because, ultimately, we wanna graph this equation on our diagram here. Remember, in earlier videos, we went from a graph that already existed or what was already shown to us, and we wanted to figure out the equation. Now we're doing the opposite. We're gonna go from an equation, and we're gonna end graphing it. So let's get started here. The y intercept of an equation is, remember, just the b term, and the slope is gonna be the m term, and you can get both of these from the slope intercept form of an equation. Remember the slope intercept form is y equals mx plus b, And if you sort of look at these two equations and and compare them, you can see that it's pretty straightforward that the m is just the negative 2 that's in front of the x and the b term is just the negative 3 that's at the end of your equation. So you just sort of compare these 2, and you can sort of pull out what those terms are. So the b is negative 3, and the m is negative 2. So how do I use this to graph? Well, the first sort of point that you can always graph is easiest is gonna be the y intercept. That's just basically where it crosses the y axis. So you just plot the point 0 comma b, whatever that number is. In this case, it's negative 3. So we're gonna plot the 0 comma negative 3, and I know that this graph is gonna cross the y axis here. Now that's not enough to figure out where sort of what this equation looks like, so I'm gonna have to plot at least one more point by using the slope. So that was the first step. Now we're gonna take a look at the second step, which is plotting one more point using the definition of the slope, which is the rise of the run. So I know this is one of my points that I can basically just use rise of a run to figure out the next set of points. So I'm gonna do that. So rise over run. So I've got my slope, which is negative 2, or if you want to express this as a fraction, it could be negative 2 over run. Remember that the negative 2 over 1. Remember the top of this fraction is the rise. The bottom is the run. So, basically, I have to go down 2 and then over 1. So if I'm going to the right like this, then I'm gonna go down 2, and it's gonna be over 1. So negative 2 and then over 1. Or if you wanted to go to the left, then you could go up 2, and that would be positive, and then over to the left one, that would be negative. Either way, it's still gonna be the same the same results. So, basically, these are 2 additional points that we can use to construct the line, and that leads us to the last step, which is now we just have to connect these points with a line. So I always like to have at least 3. You know, it just gives me, like, a good sort of a place to sort of start off with. And then what you do is you just take your straight edge or your ruler, and you're basically just gonna draw a straight line like this, and then you can extend it up and down in either direction. So this is what your equation is going to look like once you graph it. Alright? So thanks for watching. Let me know if you have any questions.

Identify the 𝒚– intercept & slope of y=−2x−3y=-2x-3y=−2x−3 . Then graph the equation.

b=−3,m=−2b=-3,m=-2b=−3,m=−2

b=−2,m=−3b=-2,m=-3b=−2,m=−3

b=23,m=−3b=\frac23,m=-3b=32,m=−3

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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Multiple Choice

Identify the 𝒚– intercept & slope of $y=-2x-3$ . Then graph the equation.

$b=-2,m=-3$

$b=-3,m=-2$

$b=$\frac$23,m=-3$

$b=2,m=-3$

Verified step by step guidance

The given equation is in the form y = mx + b, where m is the slope and b is the y-intercept.

Identify the slope (m) from the equation y = -2x - 3. Here, m = -2.

Identify the y-intercept (b) from the equation y = -2x - 3. Here, b = -3.

To graph the equation, start by plotting the y-intercept (0, -3) on the coordinate plane.

From the y-intercept, use the slope to find another point. Since the slope is -2, move down 2 units and right 1 unit from the y-intercept to plot the next point. Draw a line through these points to complete the graph.

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