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Graphing Linear Equations by Finding Intercepts

In order to graph linear equations by finding intercepts, we must remember what an x and y intercept are. So remember that in an x-intercept it’s the y that equals zero, and for the y-intercept it’s the x that equals zero. So let's put this into motion. Let's go ahead and find the x-intercept. For our x-intercept, we are going to have y equals zero. All we're going to do is plug zero in for y and solve for x. It's going to be that simple. So, we have 2x minus zero equals 6. So 2x equals 6, which implies that x equals 3. So our x-intercept can be written as (3, 0). Now, let's try to find our y-intercept. So for our y-intercept recall that our x is equal to zero. So, once again, we are going to substitute zero in for x and then solve for y. We have 2 times zero minus y equals 6. So zero minus y is just going to be negative y equals 6. So this implies that y is going to equal negative 6. To write this as a point, we've got (0, -6). Okay, so I guess now we need to actually draw the line itself. Now we have these two points and remember that this is a linear equation because notice, in this equation here, it only has a degree of 1. All I have to do is plot these two points and then draw a straight line through it. That's what a linear equation is. So we have (3, 0) and then (0, -6) which is right here. Now all I have to do is just draw a straight line through these. Which, I am hoping that you can draw a better straight line. We want to draw the arrows on it. And remember to try to draw a very long, straight line, where you don't just end it here. Remember to draw it through the whole entire graph.

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