Final answer:
The y-intercept of the equation of the line that is perpendicular to y = -3x + 10 and passes through the point (15,-5) is -10.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = -3x + 10 and passes through the point (15,-5), we first need to determine the slope of the given line. The given line has a slope of -3.
The slope of a line perpendicular to it will be the negative reciprocal, which is 1/3.
Now that we know the slope of the perpendicular line, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values (15, -5) and m = 1/3, we get the equation y - (-5) = 1/3(x - 15), which simplifies to y + 5 = 1/3x - 5.
Rearranging this equation gives us the equation of the perpendicular line, which is y = 1/3x - 10.