Algebra Know-It-ALL

324 Review Questions and Answers

Question 15-5

How can we determine the point-slope form of the equation for line PQ, based on the coor-

dinates of point P and the slope of the line?

Answer 15-5

Remember the point-slope form for a straight line in Cartesian coordinates:

y−y 0 =m(x−x 0 )

where x is the independent variable, y is the dependent variable, (x 0 ,y 0 ) are the coordinates of

a point on the line, and m is the slope of the line. We know that P= (−5,−3), so x 0 =−5 and

y 0 =−3. We also know that for line PQ, the slope m is equal to 2/5. Therefore, the point-slope

equation for line PQ is

y− (−3)= (2/5)[x− (−5)]

which can be simplified to

y+ 3 = (2/5)(x+ 5)

Question 15-6

How can we determine the point-slope form of the equation for line QR, based on the coor-

dinates of point R and the slope of the line?

Answer 15-6

We know that R= (2, 4), so x 0 = 2 and y 0 = 4. We also know that for line QR, the slope m is

equal to 5/2. Therefore, the point-slope equation for line QR is

y− 4 = (5/2)(x− 2)

Question 15-7

How can we determine the point-slope form of the equation for line PR, based on the coordi-

nates of point P and the slope of the line?

Answer 15-7

We know that P= (−5,−3), so x 0 =−5 and y 0 =−3. We also know that for line PR, the slope

m is equal to 1. Therefore, the point-slope equation for line PR is

y− (−3)=x− (−5)

which can be simplified to

y+ 3 =x+ 5