Final answer:
The equation of the line perpendicular to y=4/5x+2/5 and passing through the point (-7,3) is y = (-5/4)x - (23/4).
Step-by-step explanation:
To find the equation of the line perpendicular to y=4/5x+2/5 that passes through the point (-7,3), we first determine the slope of the given line. Perpendicular lines have slopes that are negative reciprocals of each other. Since the slope of the given line is 4/5, the perpendicular slope would be -5/4.
Now, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the point (-7, 3) and the perpendicular slope -5/4, we get:
y - 3 = (-5/4)(x + 7)
To convert to slope-intercept form (y = mx + b), we distribute and simplify:
y = (-5/4)x - (35/4) + 3
y = (-5/4)x - (35/4) + (12/4)
y = (-5/4)x - (23/4)
Therefore, the equation of the line perpendicular to y=4/5x+2/5 and passing through the point (-7,3) is y = (-5/4)x - (23/4).