Question

Write an equation of the line that is parallel to the line whose equation is 3y+7=2x and passes through point (2,6).

Answer 1

Answer:

Step-by-step explanation:

To find the equation of a parallel line, we first need to find the slope of 3y + 7 = 2x.

We need to find it because, if two lines are parallel, then that means they have the same slope.

The best way to do this is solve for y:

$3y+7=2x\\3y=2x-7\\y=\frac{2}{3}-\frac{7}{3}$

Due to the rule that in y = mx + b, m = the slope, we find that the slope is 2/3.

Now we use that slope in the same formula to find b of the line we're trying to find the equation for, and then we'll have our answer. We find b by plugging in (2, 6) for x and y:

$y = mx+b\\y=\frac{2}{3}x+b\\6=\frac{2}{3}(2)+b\\18=4+3b\\ 14=3b\\\frac{14}{3} = b$

So our line is:

$y=\frac{2}{3}x+\frac{14}{3}$