Final answer:
The equation of the line perpendicular to y = -2/5x + 3 and passing through the point (7, -1) is y = 5/2x - 37/2.
Step-by-step explanation:
The student is asking for the equation of a line that is perpendicular to a given line and passes through a specific point. The given line is y = -2/5x + 3. Since the slope of this line is -2/5, the slope of the perpendicular line must be the negative reciprocal of this value, which is 5/2. Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes, we have:
Point: (7, -1)Slope: 5/2
Plugging these values into the point-slope form yields:
y - (-1) = 5/2(x - 7)
We simplify this to get the slope-intercept form y = mx + b:
y = 5/2x - 35/2 - 1
y = 5/2x - 37/2
Therefore, the equation of the line perpendicular to y = -2/5x + 3 and passing through the point (7, -1) is y = 5/2x - 37/2.