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 (-3, 2) with slope - 6

Accepted Answer

Welcome back. I'm so glad you're here. We need to determine the equation of a line. We want to put it into slope intercept form and into point slope form. What we know about it is that it's got a slope of negative two and it passes through the 20.45. 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 you recall from previous lessons that point slope form is going to be y minus Y one where y one is the Y point that it passes through equals M. As we said, slope times x minus X one, which is that X point that it passes through. So let's look back at the things that we know, um slope M equals negative two and it passes through the point so our x one is four and ry one is five. So now we can start filling that in. It's a lot easier to start with the point slope because we don't know that be right off hand. So we do know everything else that goes into the point slope so we'll start filling that in. We know why stays as it is minus y one. That is ry one is going to be five. So we fill that in y minus five equals r M is negative two times x minus r x one is four and that's it. That is our point slope form out of the line. Now to get that into slope intercept, we're going to just keep following along with the point slope and get it. So the wise by itself, we will move that negative five over after we distribute the negative two. So we'll have negative two X plus eight X negative two times negative four. And so then now we can bring over that five and we'll have Y equals negative two X plus 13. And that is the final answer for the slope intercept form. We look at our answer choices and that matches answer choice. D Well done, you've done it, we'll catch you on the next one.

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