Question

Find the equation to the straight line which passes through the point (2,3) and is

(a) parallel to and

(b) perpendicular to the line 4x + 5y = 12​

Answer 1

answer:

the equation of the line is 2x−3y=−5.

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=32x+38

 Therefore, the slope of the line is m=32.

Now since the equation of the line with slope m passing through a point (x1,y1) is

y−y1=m(x−x1)

Here the point is (2,3) and slope is m=32, therefore, the equation of the line is:

y−3=32(x−2)⇒3(y−3)=2(x−2)⇒3y−9=2x−4⇒2x−3y=−9+4⇒2x−3y=−5

Answer 2

Step-by-step explanation:

My answer I hope you have thinking.