Write the equation of the passing through the point (6,-8) and parallel to the line y=-(5/8)x+25?

You know the slope is -5/8

y = -(5/8) x+ b
-8 = -5 (6)/8 + b
solve for b

is the answer -17/4

To find the equation of a line parallel to the given line, we need to use the fact that parallel lines have the same slope.

The given line has a slope of -5/8. So, the parallel line we're looking for will also have a slope of -5/8.

We can use the point-slope form of a linear equation to determine the equation of the line:

y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the slope.

Given that the point (6, -8) is on the line, we can substitute the values into the equation:

y - (-8) = -(5/8)(x - 6)

Simplifying further:

y + 8 = -(5/8)(x - 6)

To convert it into standard form, multiply both sides of the equation by 8 to clear the fraction:

8(y + 8) = -5(x - 6)

8y + 64 = -5x + 30

Rearranging the equation:

5x + 8y = -34

So, the equation of the line passing through the point (6, -8) and parallel to the line y = -(5/8)x + 25 is 5x + 8y = -34.