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
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To find the equation of a line parallel to y = (-1/4)x + 5, we need to find its slope. The slope of a line parallel to another line is the same as the slope of the given line. Therefore, the slope of the new line will also be -1/4.
We can use the point-slope form of a linear equation to find the equation of the line passing through the point (-8,6) with a slope of -1/4:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Plugging in the given values, we have:
y - 6 = (-1/4)(x - (-8))
y - 6 = (-1/4)(x + 8)
y - 6 = (-1/4)x - 2
y = (-1/4)x - 2 + 6
y = (-1/4)x + 4
Therefore, the equation of the line that passes through the point (-8,6) and is parallel to the graph of y = (-1/4)x + 5 is y = (-1/4)x + 4.