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.