Transcription
We're asked to convert these linear equations into slope-intercept form and then graph them on a single coordinate plane. We have our coordinate plane over here. And just as a bit of a review, slope-intercept form is a form y = mx + b, where m is the slope and b is the intercept. That's why it's called slope-intercept form. So we just have to algebraically manipulate these equations into this form.
So let's start with line A. So start with line A. So line A, it's in standard form right now; it's 4x + 2y = -8. The first thing I'd like to do is get rid of this 4x from the left-hand side, and the best way to do that is to subtract 4x from both sides of this equation. So let me subtract 4x from both sides. The left-hand side of the equation, these two 4x's cancel out, and I'm just left with 2y =. And on the right-hand side, I have -4x - 8, or -8 - 4x, however you want to do it.
Now we're almost at slope-intercept form. We just have to get rid of this 2, and the best way to do that that I can think of is to divide both sides of this equation by 2. So let's divide both sides by 2. So we divide the left-hand side by 2 and then divide the right-hand side by 2. You have to divide every term by 2. And then we are left with y = -4/2x - 8/2 = -2x - 4. So this is line A; let me graph it right now. So line A, its y-intercept is -4. So the point (0, -4) on this graph. If x = 0, y is going to be equal to -4; you can just substitute that in the graph. So 0, 1, 2, 3, 4. That's the point (0, -4). That's the y-intercept for line A.
And then the slope is -2x. So that means that if I change x by positive 1, y goes down by -2. So let's do that. So if I go over one in the positive direction, I have to go down 2; that's what a negative slope's going to do, a -2 slope. If I go over 2, I'm going to have to go down 4. If I go back -1, so if I go in the x direction -1, that means in the y direction I go positive 2, because 2 / -1 is still -2, so I go over here. If I go back 2, I'm going to go up 4. Let me just do that. Back 2 and then up 4. So this line is going to look like this. Do my best to draw it; that's a decent job. That is line A right there.
All right, let's do line B. So line B, they say 4x = -8, and you might be saying, "Hey, how do I get that into slope-intercept form? I don't see a y." And the answer is you won't be able to because this can't be put into slope-intercept form, but we can simplify it. So let's divide both sides of this equation by 4. So you divide both sides of this equation by 4. And you get x = -2. So this just means, I don't care what your y is; x is just always going to be equal to -2. So x = -2 is right there, -1, -2, and x is just always going to be equal to -2 in both directions. And this is the x-axis; that's the y-axis; I forgot to label them.
Now let's do this last equation: 2y = -8. So line C, we have 2y = -8. We can divide both sides of this equation by 2, and we get y = -4. So you might say, "Hey, Sal, that doesn't look like this form, slope-intercept form," but it is. It's just that the slope is 0. We can rewrite this as y = 0x - 4, where the y-intercept is -4 and the slope is 0. So if you move an arbitrary amount in the x direction, the y is not going to change; it's just going to stay at -4. Let me do a little bit neater. y is just going to stay at -4. Or you can just interpret it as y = -4 no matter what x is. So then we are done.