In Exercises 41–44, use the given conditions to write an equation...

Question

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (4, -7) and parallel to the line whose equation is 3x + y - 9 = 0.

Accepted Answer

Welcome back. I'm so glad you're here. We're trying to determine the equation of a line and we're going to put it into slope intercept form and point slope form. What we know about the line is that it's parallel to this line parallel to the line two, X plus Y plus four equals zero. And we know it passes through the 00.5 negative six. So let's do a quick review from previous lessons. You know that slope intercept form is going to be Y equals M X plus B, where M is the slope and B is the y intercept and that our point slope form is going to be in the form Y minus Y. One, that's r Y point that it passes through equals M slope times x minus x. One. That's the X point that it passes through. And so we've got those formulas and we know it's parallel to this other line, but this other line isn't in either form yet. So the first thing we're going to do is put it into slope intercept form. So it's easy to identify what that and what that slope is. So we want to get why by itself. We're going to move the four to the other side and the two X to the other side. So that'll give us why equals negative two X minus four. Great. That's in slope intercept form. And it's easy to identify the slope negative two. Because what we know about parallel lines is that parallel lines have identical slopes. Their slopes are the same thing. So our line's slope is the same as the other one. It's negative two. So we know that our M. Is going to be negative two for both of these equations. Great. What else do we know? We know that it passes through this 20.5? Negative six. Well in the point slope format we know that that five is going to be our X point and we know that that negative six is going to be our Y point. And so now we can just copy everything else down. The Y stays as it is the minus stays there equals negative two, is our m parentheses X minus. And then that five, we can simplify this just a little bit instead of Y minus negative six. We can say y plus six and then bring the rest down equals negative two parentheses X minus five. And that is our point slope format. And now we'll just keep going with this same point slope format to get it into the slope intercept form where we just want the Y by itself. So in order to do that, we're going to move that six over. But first let's get rid of the parentheses. So we'll distribute the negative two times X and times the five. So negative two times negative five gives us positive 10. Now we've got y plus six equals negative two, X plus 10. We'll bring the six over and we've got the y by itself Y equals negative two X plus four. And that is the final answer for our slope intercept form and, yep, that negative two matches. We look at our answer choices in this matches answer choice a well done. You've done it, we'll catch you in the next one.

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