Graph the given linear equation. − 2 x = y − 6 -2x=y-6

this problem we are asked to graph the following linear equation. Now what I'm going to do is sketch out my own graph, where we're going to have a y axis, and we're going to have an x axis. Now on my graph, I like to mark five points left, right, up, and down. So we're going to go one, two, three, four, five in the positive x direction, and we'll imagine these are one, two, three, four, five. Then we'll go one, two, three, four, five in the negative direction. So that'd be negative one, negative two, and this keeps on going. Then we'll have one, two, three, four, five in the positive y direction. And then we'll have one, two, three, four, five in the negative y direction. So now we've gone ahead and sketched our graph, and now we can try to graph our equation. Now to do this, I need to choose x values that are going to work. Now the first x value that I'm going to try is an x value of negative one. So what that means is I need to take my x and replace it with negative one. So you're gonna have negative two times negative one equals y minus six. Now this is going to give me positive two is equal to y minus six, and I can go ahead and add that six on both sides of the equation. That's gonna give me y is equal to two plus six, which is eight. Now notice that when x equals negative one, y equals eight. This is the ordered pair that we just found. Now this is going to be a bit off the graph that we've sketched. This goes down to negative or this goes up to five, I should say. But if we had six, seven, eight, we would show up right somewhere up top on the y axis. So we would get a point that looks something like this if we were to plot negative one, eight. Now I'm not gonna keep this point on here, or I'm not gonna use this necessarily as a specific reference, but this in general shows me what my graph is going to look like. It's gonna be a relatively steep line. So since we've gone ahead and found this, let's go ahead and find some more points that are going to be on the graph that we've sketched. So now I'll try an x value of zero. It's gonna be right about here in the center. So what that means I need to take my x and replace it with zero. So that's y minus six, negative two times zero is zero, and then I can add the six on both sides of the equal sign. That's gonna give me that y equals six. So when x is equal to zero, y is equal to six. That's interesting. So even if we go to an x value of zero, we still end up with a point that's slightly above our axis here. We end up with zero, six. So let's now choose one. Well, if I choose one, I just need to take this x and replace it with one. So we have negative two times one is equal to y minus six. That's gonna give me negative two equals y minus six. I can add the six on both sides of the equal sign, giving me that y is equal to six minus two or negative two plus six, which is four. So when x is equal to one, y is equal to four. Now we finally end up somewhere that's actually on the graph. So we get one, and then we get four, which is gonna show up on our graph. And because I've been getting so many points off the graph, I'm gonna choose another positive x value. So I'm actually gonna go up to two this time. Remember, we're just plotting these points to get a general sense of what our line's going to look like. So going back to my equation, we get negative two times two is equal to y minus six. It's gonna give me negative four. That's negative two times two, y minus six. We can add the six on both sides of the equal sign, giving me that y is equal to negative four plus six, which is two. So we're gonna have a point at two, two. And this is definitely gonna be on our graph. So when x is equal to two, y is also equal to two. And I can already see what this line is going to look like. So we're gonna get a line that goes through these points, giving us the solution to our problem. And even if I were to get rid of these other two points that showed up off the graph, we would still have enough to graph our line on what we have. So any graph you see that looks like this, or if you're free handing this, you can just sketch the graph yourself. That is what the line's going to look like based on the equation we have. I hope you found this video helpful.

4. Graphs and Functions

Graph Linear Equations in Two Variables

Intermediate Algebra

4. Graphs and Functions

Graph Linear Equations in Two Variables

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Multiple Choice

Graph the given linear equation.
$- 2 x = y - 6$

Graph of the linear equation -2x = y - 6 shown as a downward sloping line on an x-y coordinate plane.

Graph of the linear equation −2x = y − 6 shown as a line passing through points on a coordinate plane.

Graph of the linear equation -2x = y - 6 showing a vertical line at x = 3 on a coordinate plane.

Graph of the linear equation -2x = y - 6 shown as a vertical line at x = 3 on a coordinate plane.

Verified step by step guidance

Start with the given linear equation: $-2x = y - 6$.

Rearrange the equation to solve for $y$ in terms of $x$. Add 6 to both sides to isolate $y$: $y = -2x + 6$.

Identify the slope and y-intercept from the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Here, the slope $m = -2$ and the y-intercept $b = 6$.

Plot the y-intercept point $(0, 6)$ on the coordinate plane.

Use the slope $-2$ (which means down 2 units and right 1 unit) to find another point starting from the y-intercept, then draw a straight line through these points to graph the equation.

5:51m

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Struggling with Intermediate Algebra?

Graph the given linear equation.−2x=y−6-2x=y-6

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Graph the given linear equation.
$- 2 x = y - 6$