Question

(i) Find the equation of the line through the point (-2, 3) and parallel to the line
3x + 5y - 4 = 0.
(ii) Find the equation of the line through the point (1, -2) and perpendicular to the line
x - 2y + 3 = 0.​

Answer 1

Answer:

Step-by-step explanation:

First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:

2x−3y+8=0

⇒−3y=−2x−8

⇒3y=2x+8

⇒y=

3

2

​

x+

3

8

​

Therefore, the slope of the line is m=

3

2

​

.

Now since the equation of the line with slope m passing through a point (x

1

​

,y

1

​

) is

y−y

1

​

=m(x−x

1

​

)

Here the point is (2,3) and slope is m=

3

2

​

, therefore, the equation of the line is:

y−3=

3

2

​

(x−2)

⇒3(y−3)=2(x−2)

⇒3y−9=2x−4

⇒2x−3y=−9+4

⇒2x−3y=−5

Hence, the equation of the line is 2x−3y=−5.