Write the equation of the line that passes through the point (-5, 1) and is PERPENDICULAR (slope is opposite reciprocal) to the line y=(-5/3)x-7.
The given line has a slope of -5/3. A line that is perpendicular to this line will have a slope that is the opposite reciprocal of -5/3, which is 3/5.
Using the point-slope form of equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can plug in the values we know to find the equation of the line:
y - 1 = (3/5)(x - (-5))
Simplifying this equation:
y - 1 = (3/5)(x + 5)
y - 1 = (3/5)x + (3/5)(5)
y - 1 = (3/5)x + 3
Adding 1 to both sides to isolate y, we get:
y = (3/5)x + 4
Therefore, the equation of the line that passes through the point (-5, 1) and is perpendicular to y=(-5/3)x-7 is y = (3/5)x + 4.