Final answer:
The equation of the line that passes through the point (6,8) and is perpendicular to y = -1/5x - 8 in slope-intercept form is y = 5x - 22.
Step-by-step explanation:
To find the equation of a line perpendicular to y = -1/5x - 8, we'll first determine the slope of the given line. The slope of y = -1/5x - 8 is -1/5. Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we're looking for will be the negative reciprocal of -1/5, which is 5.
Now that we have the slope (m = 5) and a point the line passes through (6,8), we can use the point-slope form of a line equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Plugging in the values (x₁ = 6, y₁ = 8, m = 5):
y - 8 = 5(x - 6)
y - 8 = 5x - 30
y = 5x - 30 + 8
y = 5x - 22
Hence, the equation of the line in slope-intercept form that passes through (6,8) and is perpendicular to y = -1/5x - 8 is y = 5x - 22.