Final answer:
The equation is y = -5/2x + 31/2. To find the equation of a line that is parallel to y = -5/2x + 10 and passes through the point (6,8), we can use the point-slope formula.
Step-by-step explanation:
To find the equation of a line that is parallel to y = -5/2x + 10 and passes through the point (6,8), we need to find the slope of the given line and then use it to form the equation of the new line.
The given line has a slope of -5/2, so the new line will have the same slope since it's parallel. Using the point-slope formula, we can plug in the values of the given point (6,8) and the slope (-5/2) to find the equation:
y - y₁ = m(x - x₁)
y - 8 = -5/2(x - 6)
y - 8 = -5/2x + 15/2
y = -5/2x + 15/2 + 8
y = -5/2x + 31/2