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We first need to write the equation of the line with slope 2/3 and that goes through the point (3,5). To do this, we need to find the y-intercept. Using the point-slope form of a linear equation,
y - y1 = m * (x - x1), substituting (x1, y1) with (3,5) and m with 2/3
y - 5 = 2/3 (x - 3).
Now we have to simplify it, using the distributive property on the right side of the equal sign:
y - 5 = 2/3 x - 2. (Remember 2/3 * 3 = 2)
Add 5 to both sides of the equal sign.
y - 5 + 5 = 2/3 x - 2 + 5
y = 2/3 x + 3.
Now we have to find the y-coordinate of the point on the line when x = 6. Substitute 6 for x in the above equation.
y = (2/3) (6) + 3
y = 4 + 3
y = 7.
So the y-coordinate of the point the line goes through when x = 6 is 7.