Final answer:
The equation of the line perpendicular to y = 5x + 4 and passing through the point (1, 2) is y = -1/5x + 2.2. None of the provided options exactly matches the derived equation. The closest option, which requires a correct y-intercept calculation, is y = -1/5x + 3, but an accurate calculation shows the y-intercept should be 2.2.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another, you first need to determine the slope of the given line. The line given is y = 5x + 4, which means the slope (m) is 5. For a line to be perpendicular, its slope must be the negative reciprocal of the slope of the given line, so our slope will be m = -1/5.
Now, using the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, we can plug in our values. So we have y - 2 = -1/5(x - 1). Simplifying, we get y - 2 = -1/5x + 1/5. Adding 2 to both sides yields the linear equation in slope-intercept form, which is y = -1/5x + 2 1/5 or y = -1/5x + 2.2.
Matching the choices provided in the question, the closest option is y = -1/5x + 3; however, it does not fully match our derived equation. We will need to confirm the correct y-intercept by substituting the point (1, 2) into the equation y = -1/5x + b to solve for 'b'. Plugging in the point gives us 2 = -1/5(1) + b which simplifies to b = 2 + 1/5. Thus, b = 2.2 and our correct equation is y = -1/5x + 2.2.