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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:

[tex]3y+7=2x\\3y=2x-7\\y=\frac{2}{3}-\frac{7}{3}[/tex]

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:

[tex]y = mx+b\\y=\frac{2}{3}x+b\\6=\frac{2}{3}(2)+b\\18=4+3b\\ 14=3b\\\frac{14}{3} = b[/tex]

So our line is:

[tex]y=\frac{2}{3}x+\frac{14}{3}[/tex]

The equation of the line in slope-intercept form is: y = 2/3x + 14/3.

What is the Slope-intercept Equation?

Slope-intercept equation of a line where m is the slope and b is the y-intercept is, y = mx + b.

First, rewrite 3y + 7 = 2x in slope-intercept form and find its slope:

3y + 7 = 2x

3y = 2x - 7

y = 2/3x - 7/3

Slope would be 2/3.

Slope of parallel lines are teh same, therefore, plug in m = 2/3 and (a, b) = (2, 6) into y - b = m(x - a) to find the equation of the line that is parallel to 3y + 7 = 2x.

y - 6 = 2/3(x - 2)

Rewrite in slope-intercept form

y - 6 = 2/3x - 4/3

y = 2/3x - 4/3 + 6

y = 2/3x + 14/3

Therefore, the equation of the line in slope-intercept form is: y = 2/3x + 14/3.

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