Question

The equation of the line A is 3x+2y=10.line B is parallel to line A and passes through the points (4,6).find the equation of the line B.​

Answer 1

Answer:
`y=-(3)/(2)x+12`

Explanation:

To find the equation of line B, we need to find the slope first, then the y-intercept. We first want to convert line A into slope-intercept form, so we can find the slope.

`3x+2y=10` [subtract both sides by 3x]

`2y=10-3x` [divide both sides by 2]

`y=5-(3)/(2)x`

With the slope-intercept form of line A, we can see that the slope is
`-(3)/(2)`. We take the slope and the given point (4,6) to find the y-intercept of line B.

`y=-(3)/(2)x+b` [plug in (4,6)]

`6=-(3)/(2)(4)+b` [multiply]

`6=-6+b` [add both sides by 6]

`b=12`

With the y-intercept, we know the equation for line B is
`y=-(3)/(2)x+12`.