(i) Find the equation of the line through the point (-2, 3) and parall

1.	(i) Find the equation of the line through the point (-2, 3) and parallel to the line3x + 5y - 4 = 0.(ii) Find the equation of the line through the point (1, -2) and perpendicular to the linex - 2y + 3 = 0.
Answer» 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.

(i) Find the equation of the line through the point (-2, 3) and parallel to the line3x + 5y - 4 = 0.(ii) Find the equation of the line through the point (1, -2) and perpendicular to the linex - 2y + 3 = 0.

Answer»

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=

Therefore, the slope of the line is m=

Now SINCE the equation of the line with slope m passing through a POINT (x

) is

y−y

=m(x−x

)

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

, therefore, the equation of the line is:

y−3=

(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.