Use the given conditions to write an equation for each line in...

Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−2, −4) and (1, −1)

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 first we need to note that our line passes through the points negative six, negative two and the point negative 44. So 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. Sub one. And now from here we need to assign the X sub one, Y sub one and X up to Y sub two to either point. So I'm going to let our first point B the X sub one and Y sub one. So that means our second point must be the X. Up to and Y sub two. Now it's important to note that it doesn't matter which point is assigned what, as long as it's kept consistent throughout the problem. So now plugging in this information into our slope formula we have in the numerator, Y sub two which is four minus Y sub one which is negative two. And in the denominator we have X sub two which is negative four minus x sub one which is negative six. And now simplifying, we have four minus negative two which is positive six divided by negative four minus minus negative six gives us positive 26 divided by two gives us a slope of three. And now from here we just need to recall our point slope form which is why I minus y. Sub one is equal to slope M times the quantity of x minus x. Of one. And now from here we just need to plug in our information that we have so far. So we have y minus Y. Sub one which is negative two is equal to slope M. Which we found us three times the quantity of x minus X. Sub one which is negative six. Now we can just simplify and factor in this three. So we have Y plus two is equal to three X plus 18. And now from here to get our equation into slope intercept form, we have to transpose this positive two to the right side. So subtracting two from both sides, we get a final answer of Y is equal to three X plus 16 which is our answer here for choice. C Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−2, −4) and (1, −1)

Key Concepts

Slope of a Line

Point-Slope Form of a Line

Slope-Intercept Form of a Line

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