Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-5,4), m = -3/2

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Accepted Answer

Welcome back. I am so glad you're here. We are asked to find the equation of a line passing through the point negative 73, having a slope slope is M equal to negative five thirds. And were to write the equation in standard form, we recall from previous lessons that the standard form for the equation of a line is A X plus B Y equals C. Or in other words, we want all the X and Y terms together on one side of the equation and the constant terms on the other. So how do we get from having a point and a slope to standard form? Will we recall from previous lessons that we have point slope form of a line? That is why I minus Y one Equals M. Times X -X one. And we look at our point R point gives us our X one and Ry one and our slope, as we said is M so now we can just plug everything in. So we have why minus we know that? Why one is three equals M is negative five thirds times X minus X one is negative seven. Now it's just a matter of simplifying. On the left hand side, we can bring down Y minus three for now and negative five thirds times X and X minus negative seven is X plus seven. And now we can get rid of our fraction by multiplying everything on both sides by that denominator by three. So we're going to multiply both sides by three. Now, we can do that three times Y is three, Y and three times negative three is minus nine equals. And on the right hand side, negative five thirds times three simplifies to negative five and then bring down the X plus seven. Now, on the right, we can distribute this negative five to the X and to the seven. So I'll bring down three Y minus nine equals negative five times X is negative five X and negative five times seven equals negative 35. Now to get this into standard form, we want the excess and wise together on one side, let's bring this negative five X to the left hand side will add five X to both sides so that the X terms will be positive, we can keep the Y term on the left hand side with the X term. And then let's bring this nine over to the right, so that the constant terms are together on the right hand side of the equation. So on the left will have five X plus three Y and there's those nines cancel out over there. On the right hand side, those five X's cancel out and we have negative 35 plus nine which equals negative 26. And here is our equation in the standard form. So we're looking at our answer choices for five X plus three, Y equals negative 26. And that matches with answer choice B well done. We'll catch you on the next one.

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-5,4), m = -3/2

Verified Solution

Key Concepts

Point-Slope Form

Slope-Intercept Form

Standard Form