A perpendicular equation to a line equation, has the reciprocal and opposite slope
We have:
[tex]y=\frac{4}{7}x+6[/tex]So the new equation will have the slope -7/4:
[tex]y_p=-\frac{7}{4}x+b[/tex]b is the intercept, the point where the line crosses the y-axis. We can find the intercept using the point (0,-2). We replace x = 0 and y = -2 into the equation above and we have that b = -2.
The equation is:
[tex]y_p=-\frac{7}{4}x-2[/tex]