Final answer:
The equation of the line perpendicular to y = 3x - 10 and passing through the point (3, 4) is y = (-1/3)x + 5.
Step-by-step explanation:
To find the equation of a line perpendicular to y = 3x - 10 that passes through the point (3, 4), we first determine the slope of the original line. The slope m of the given line is 3. For a line to be perpendicular to this one, its slope must be the negative reciprocal, so the new slope will be -1/3.
Next, we use the point-slope form of a line's equation which is y - y1 = m(x - x1), where (x1, y1) is a known point on the line and m is the slope. Substituting our points (3, 4) and our new slope -1/3, we get:
y - 4 = (-1/3)(x - 3)
Now we simplify to put it into slope-intercept form. Hence:
y - 4 = (-1/3)x + 1
y = (-1/3)x + 5
The equation of the line perpendicular to y = 3x - 10 and passing through (3, 4) is y = (-1/3)x + 5.