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, 6) and perpendicular to the line whose equation is y = (1/3)x + 4

Accepted Answer

Welcome back. I'm so glad you're here. We are trying to determine the equation of a line and we want to put it into slope intercept form and point slope form things that we know about this line. Well, we know it's perpendicular to the line at y equals 3, 15 X plus eight and it passes through the 80.7 negative two. Let's do a quick review from previous lessons. You've learned that slope intercept form of a line is shown as Y equals M X plus B. And we know that the point slope formula for a line is going to be why one, nope, sorry, why minus? Why? One Equals M. Times X -X one. And we know with both of those that M is the slope. And we also know that when we're talking about perpendicular slope is going to be the negative inverse. So if it's perpendicular to this line, Y equals 3/5 explicit. Well, that's already in slope intercept form so that M is going to be right in front of the X. And so our lines slope is going to be the negative inverse of 3/5. So our line is going to have the slope of M equals negative 5/3. So we can fill that in both of these negative 5/3 is going to be our slope. And we also know that it passes through this .7, Well, we can fill that in for um this point slope formula, so the X one is going to be seven and the y one is going to be negative two and then we just bring down the Y and X and this one is almost done. So we've just got to simplify this, y minus negative is going to be Y plus two equals negative five thirds times x minus seven. And that one is done. That's in the formula or in the format that we want it to be And now to get it into slope intercept form, we just want to get that Y by itself on the left. So we're going to take that negative 5/3 and we're going to distribute it. And so we've got negative five thirds X plus negative times a negative 35/3 and y plus two on the left side and then we'll subtract two from both sides. So if we've got 35/3 minus two, we can take that times 3/3. So in effect times one and that would give us 3rd minus six thirds, which equals 29 3rd. And so we've got the Y by itself, Y equals and then we've got negative five thirds X plus 3rd. Those are our final answers for those two formulas. We look at our answer choices and that matches answer choice, hey, well done, we'll catch you in the next one

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