Write the equation of the line that passes through the given point and is parallel to the graph of the given equation: (-8,6); y = -1/4 x + 5
The given equation is y = -1/4x + 5.
Since the line we are trying to find is parallel to this given equation, the slope of the line will be the same, which is -1/4.
Using the point-slope form of a linear equation (y - y₁ = m(x - x₁)), where (x₁, y₁) is the given point (-8, 6), and m is the slope (-1/4), we can substitute these into the equation:
y - 6 = -1/4(x - (-8))
Simplifying:
y - 6 = -1/4(x + 8)
Expanding:
y - 6 = -1/4x - 2
Adding 6 to both sides:
y = -1/4x + 4
Therefore, the equation of the line that passes through the point (-8, 6) and is parallel to the graph of y = -1/4x + 5 is y = -1/4x + 4.