Final answer:
To find the equation of a line parallel to y = 3x + 6 and passing through (2,10), we use the point-slope form of a linear equation. Substituting the values into the formula, we find that the equation of the parallel line is y = 3x + 4.
Step-by-step explanation:
To find the equation of a line that is parallel to the graph of y = 3x + 6 and passes through the point (2, 10), we can use the fact that parallel lines have the same slope.
The given equation has a slope of 3, so the parallel line will also have a slope of 3.
Using the point-slope form of a linear equation, we can substitute the slope and the coordinates of the given point into the formula to find the equation of the parallel line:
y - y1 = m(x - x1)
Substituting the values into the formula:
y - 10 = 3(x - 2)
Simplifying the equation:
y - 10 = 3x - 6
y = 3x + 4
Therefore, the equation of the line that passes through (2,10) and is parallel to the graph of y = 3x + 6 is y = 3x + 4.