Question

The line y = ax + b is parallel to the line y = 2x - 6 and passes through the point (-1, 7). Find the value of a and b.​

Answer 1

Answer

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=32​x+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

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