In Exercises 11–38, use the given conditions to write an equation...

Question

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−3, 6) and (3, −2)

Accepted Answer

Hey everyone here we are asked to write an equation for the line in slope intercept form by first going through point slope form. So we first want to note that our line passes through the point negative 20 and the 200.4 negative nine. Now we want to find our slope. So we need to recall our slope formula which states that slope M. Is equal to the quantity of Y sub two minus Y sub one divided by the quantity of X sub two minus X of one. Now we need to assign this X one, Y one and X two and Y sub two to our given points. So I'm going to let our first point B. The X one and Y sub one point. So then our second point must be the X. Up to and Y sub two point. Now it's important to note that it doesn't matter which point is assigned to what as long as it's kept consistent throughout the problem. So next we can plug in this information into our slope formula. So in the numerator we have Y sub two which is negative nine minus Y. Sub one which is zero. And in the denominator we have X sub two which is four minus X. Sub one which is negative two. And now we can just simplify. So we have a negative nine minus zero which is negative nine divided by four minus negative two, which is positive six and negative nine divided by six simplifies to negative three divided by two. And so from here we just have to recall our point slope form. So that is why minus Y. Y. Sub one is equal to the slope M. Times the quantity of x minus X. Sub one. And so from here we can just plug in the information we already have. So we have y minus Y sub one which is zero is equal to slope M. Which we found as negative three halves times the quantity of X minus X. Sub one which is negative two. And now we just have to simplify and factor in this negative three halves to get our equation into slope intercept form. So we have Y is equal to negative three halves times X plus negative three halves times positive two. So our final equation simplifies to why is equal to negative three halves X minus three. Which is our answer here for choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−3, 6) and (3, −2)

Key Concepts

Point-Slope Form

Slope-Intercept Form

Calculating Slope

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