Question

A given line has the equation .

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

Answer 1

It looks like the equation of the given line is missing from your question. Please paste it in.

Meanwhile here's how to get the answer once you have the given line:

- If the given line has slope m1, then a perpendicular line has slope m2 = −1/m1.
- A line with slope m2 that passes through (0,9) has equation y = m2 x + 9.
- Special cases:
- If the given line is vertical (x = a), its slope is undefined; a perpendicular line is horizontal with equation y = 9.
- If the given line is horizontal (y = b), its slope is 0; a perpendicular line is vertical x = 0 (not expressible in slope-intercept form).

Examples:
- Given y = 2x + 1 → perpendicular slope = −1/2 → answer y = −(1/2)x + 9.
- Given 3x − 4y = 12 → slope = 3/4 → perpendicular slope = −4/3 → answer y = −(4/3)x + 9.

Send the given line and I’ll compute the exact equation.