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: $y=-\frac{3}{2}x+12$

Step-by-step 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]

$y=5-\frac{3}{2}x$

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

$y=-\frac{3}{2}x+b$            [plug in (4,6)]

$6=-\frac{3}{2}(4)+b$         [multiply]

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

$b=12$

With the y-intercept, we know the equation for line B is $y=-\frac{3}{2}x+12$.