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 general form. Passing through (4, −7) and perpendicular to the line whose equation is x − 2y – 3 = 0

Accepted Answer

Hey everyone here we are asked to write the equation of a line in both slope intercept and point slope form using the fact that the line passes through the 0.0. negative one and it is perpendicular to the line, X plus three, y minus seven equals zero. Now we want to start by focusing on finding the slope for the line. But to do this we need to first find the slope for the perpendicular line and now to do that we need to first recall the slope intercept form which is why is equal to M. X plus B. And now from here we can rearrange the perpendicular line to slope intercept form so we can clearly see what its slope is. So doing so we want to get three y by itself. So we'll transpose both the X and the negative seven to the right side of the equation giving us three, Y is equal to negative X plus seven, dividing both sides by three. To get y by itself we get Y is equal to negative one third X plus seven thirds. And now here we can clearly see that the slope for our perpendicular line, which I will denote as M sub one is equal to negative one third. And now from here to find the slope of the line of which we're looking for. We can use the formula M sub one times M sub two is equal to negative one. And now we can plug in the slope we just found to give us negative one third times M sub two is equal to negative one, dividing both sides by negative one third gives us the slope of positive three. And now from here we see that we have a slope and we are also given one point so we can write the equation of a line in point slope form. And we need to recall that point slope form is why minus Y. Sub one is equal to M times the quantity of x minus X. Sub one. And now plugging in the information we already have. We get why minus Y. Sub one which is negative one equals M which is three times the quantity of x minus X. Sub one which is four. So just simplifying this really quickly we get the point slope form of Y plus one is equal to three times the quantity of x minus four. And now we have point slope form here. But we need to also get slope intercept form and to do this. All we need to do is transpose this positive one and factor in this three here. So this gives us first Y plus one is equal to three x minus 12. And now subtracting one from both sides, we get Y is equal to three x minus 13. As our answer for the slope intercept form and using both of these equations, we have the answer choice of D. 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 general form. Passing through (4, −7) and perpendicular to the line whose equation is x − 2y – 3 = 0

Key Concepts

Point-Slope Form of a Line

Slope of a Line from General Form

Perpendicular Lines and Their Slopes

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