Everything Maths Grade 11

16.5 CHAPTER 16. GEOMETRY

SOLUTION

Step 1 : Label the points

(x 1 ; y 1 ) = (−3;2)

(x 2 ; y 2 ) = (5;8)

Step 2 : Calculate the gradient

m =

y 2 − y 1

x 2 − x 1

=

8 − 2

5 − (−3)

=

6

5 + 3

=

6

8

=

3

4

Step 3 : Determine the equation of the line

y− y 1 = m(x− x 1 )

y− (2) =

3

4

(x− (−3))

y =

3

4

(x + 3) + 2

=

3

4

x +

3

4

.3 + 2

=

3

4

x +

9

4

+

8

4

=

3

4

x +

17

4

Step 4 : Write the final answer

The equation of the straight line that passes through (−3;2) and (5;8) is y =

3

4 x +

17

4.

Equation of a Line Through One Point and

Parallel or Perpendicular to Another Line

EMBCM

Another method of determining the equation ofa straight-line is to be given one point, (x 1 ; y 1 ), and to
be told that the line is parallel or perpendicularto another line. If the equation of the unknown line is