Answer:
the equation of the line parallel to y = 3x - 2 and passing through the point (1, 9) is y = 3x + 6.
Explanation:
To find the equation of a line that is parallel to the line y = 3x - 2 and passes through the point (1, 9), we can use the fact that parallel lines have the same slope.
The slope of the line y = 3x - 2 is 3 because it's in the form y = mx + b, where "m" represents the slope.
So, the line we're looking for also has a slope of 3. Now, we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point (1, 9) and m is the slope (which is 3).
Substitute these values into the equation:
y - 9 = 3(x - 1)
Now, distribute the 3 on the right side:
y - 9 = 3x - 3
To isolate y, add 9 to both sides of the equation:
y = 3x - 3 + 9
y = 3x + 6
So, the equation of the line parallel to y = 3x - 2 and passing through the point (1, 9) is y = 3x + 6.