Write an equation in point-slope form and slope-intercept form...

Question

Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.

Accepted Answer

hey everyone here we are asked to find the equation of the line in point slope form and slope intercept form, which passes through the point negative four negative 11 and is perpendicular to the line, X minus six, Y plus 24 is equal to zero. Now our first step here is to rearrange this given equation into slope intercept form. So we can see its slope and then find the slope of our unknown line. So first we need to recall that slope intercept form is Y is equal to M X plus B. So now we need to manipulate this equation here so we can start getting y alone by first adding six Y to both sides. So we have six, Y is equal to X plus 24. And now to get y completely alone, we need to divide both sides by six and we see that Y is equal to 16 times X plus 24. And so now we can see that the slope of this perpendicular line is 1/6 and we can denote this slope as M sub one, so M sub one is equal to 1/6. And now we need to recall that the slope of a perpendicular line in relation to the unknown line is M sub two is equal to negative one divided by M sub one. So it's the negative inverse of the perpendicular slope. And so now to find our slope here, we just need to plug in the perpendicular slope. So so we have negative one divided by 16, which tells us that our slope is negative six. And now we can easily find our equation in point slope form since we now have our slope and we have one point which it passes through. So we need to recall that point slope form is why minus Y sub one is equal to M the slope. The quantity of x minus X. Sub one. So now we can plug in our point into the Y sub one and X sub one variables here and then plug in our slope which we found. So doing this, we have y minus Y sub one which is negative 11 is equal to the slope which is negative six times equality of x minus X. Sub one, which is negative four. Now quickly simplifying, we see that in point slope form. Our equation is Y plus 11 is equal to negative six times the quantity of X plus four. And now we can rearrange this equation into slope intercept form to get our second equation. So doing this, we can first factor in this negative six. So we have Y plus 11 is equal to negative six X minus 24. And now subtracting away Seven from both sides, we have the slope intercept form of Y is equal to -6 X -35. And now we have found both forms of our line. We have point slope form and the slope intercept form. Leaving us with answer choice. B thanks for watching. I hope you found this video helpful and I'll see you again next time.

Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.

Key Concepts

Slope of a Line

Perpendicular Lines and Their Slopes

Point-Slope and Slope-Intercept Forms of a Line

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