Graph the given linear equation. 3 x − 2 y = 4 3x-2y=4

this problem we are asked to graph the given linear equation. Now it doesn't appear that I have a graph given to me specifically in this problem, so I'm going to make my own. So we're going to have a y axis, and then we're going to have an x axis. Now on this graph, I'm going to label a few points. I like to go by five. So we're going to go one, two, three, four, five for the x axis, and we're gonna go in the negative direction, one, two, three, four, five. We're gonna go in the positive y direction, one, two, three, four, five. And then in the negative y direction, we're going to go five as well. So this is gonna be our graph. Now what I need to do is graph the equation that I see, and I can do this by choosing once. Now I'm just going to assume that this is gonna go up by one. So it's gonna go one, two, three, and this is just gonna keep going to the right, and then negative one, negative two, negative three to the left. I'm not gonna sketch those just so it doesn't look too crowded, but this is how I'm going to graph it. So going to my equation right here, what I need to do is choose x values. Now the x value I'm gonna start with is negative one. So for negative one, let's go ahead and plug this into our equation. So going to have three times negative one minus two y is equal to four. Three times negative one is negative three, and then we can add the three on both sides of the equal sign. That'll get the threes to cancel, giving me negative two y is equal to three plus four, which is seven. And then we can divide this negative two on both sides of the equation. So that's going to give us y is equal to negative seven halves. Now what this ends up coming out to, so if I go ahead and recognize that two can go into six three times, then we'll just have another half of one, so this is going to be 3.5 or negative 3.5 actually, because and that makes sense because two can divide it into six three times, and so we can divide it into seven three and a half times. So this is what we get for our y. So when x is equal to negative one, y is equal to negative 3.5. So if I go over to this graph that I sketched, well, I can see that x is negative one that we've already drawn, and I need to go down one, two, three, but then I need to go about halfway to three as well, so right about there. And notice that our point shows up on our graph, and this is going to be negative one and then negative, and then we'll go seven halves or 3.5. And so this is what our point's going to look like. Now I'm gonna choose another point. Let's say where x is zero. So in this case, we're going to have three times zero minus two y is equal to four. And that's going to give us zero minus two y equals four, which is negative two y equals four. Then divide out that negative two on both sides of the equation, giving me that y is four over negative two, which is negative two. So when x is zero, y is negative two, which is going to give me a point, and an x of zero and a y of negative two. So now I'm going to choose one more point just to secure this line, and I'm going to choose an x value of one. So So we've chosen zero, negative one, and now let's choose one. So because we have one, I'm going to plug one in for x in this equation. So that's going to give me three times one minuteus 2y is equal to four. It's going to give us three minuteus 2y equals four. I can subtract the three on both sides of the equal sign, giving me negative two y equals four minus three, which is one. And then I can divide out that negative two, which is going to get the negative twos to cancel, giving me that y is equal to negative one half. So when x is one, y is gonna be negative one half, which is the same thing as about negative 0.5. So if I go ahead and go over to my graph, when x is equal to one, y is going to be exactly on the halfway or actually, this is negative point five, so it's gonna actually be halfway down. Right? So it's gonna be halfway down, meaning that we'll have another point on our graph that we can sketch. And after sketching these points, I can just draw a line to connect them. I think three points is enough. So that's going to give me my line, and this is what we are looking for. So that will be the answer to this problem. So if you see a graph that looks like this, if you have a multiple choice, or if you just have to sketch this on a free graph, this is how you go about doing it. I went ahead and sketched the whole graph for you so you could see this process, but this is the strategy for graphing linear equations.

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Graph Linear Equations in Two Variables

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Graph the given linear equation.
$3 x - 2 y = 4$

Graph of the linear equation 3x - 2y = 4 shown as a downward sloping line on an x-y coordinate plane.

Graph of the vertical line x = 3 on a coordinate plane with labeled x and y axes.

Graph of the linear equation 3x - 2y = 4 showing a line passing through points (-2, -5) and (2, 4) on a coordinate plane.

Graph of the linear equation 3x - 2y = 4 shown as an orange line crossing the coordinate plane.

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Start with the given linear equation: $3x - 2y = 4$.

Rewrite the equation in slope-intercept form $y = mx + b$ by isolating $y$. Subtract \$3x$ from both sides to get $-2y = -3x + 4$, then divide every term by $-2$ to get $y = \frac{3}{2}x - 2$.

Identify the slope $m = \frac{3}{2}$ and the y-intercept $b = -2$. This means the line crosses the y-axis at $(0, -2)$ and rises 3 units for every 2 units it moves to the right.

Plot the y-intercept point $(0, -2)$ on the coordinate plane. From this point, use the slope to find another point by moving up 3 units and right 2 units, landing at $(2, 1)$.

Draw a straight line through the points $(0, -2)$ and $(2, 1)$ extending in both directions. This line represents the graph of the equation $3x - 2y = 4$.