To find the equation of a line passing through the point (2, 17) that is parallel to the line y = 4x + 7, you can use the fact that parallel lines have the same slope. In the equation y = 4x + 7, the slope is 4. So, the parallel line will also have a slope of 4.
Now, you can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point (2, 17), and m is the slope (which is 4).
Plug in the values:
y - 17 = 4(x - 2)
Now, you can simplify and write it in standard form if needed:
y - 17 = 4x - 8
To write it in standard form (Ax + By = C), you can move all terms to one side:
4x - y = 8 - 17
4x - y = -9
So, the equation of the line passing through (2, 17) and parallel to y = 4x + 7 is 4x - y = -9.