To find the equation for this line, we are going to use point-slope form. First, to find the perpendicular slope, we need to find the slope of the line 4y=5x - 8. To do this, we must transform this equation into slope-intercept form so we can determine the slope.
4y=5x-8
We should divide both sides of the equation by 4 to put the equation into slope-intercept form.
4y/4 = 5x/4 - 8/4
y = 5/4x - 2
Therefore, we can determine that the slope of this equation is 5/4. The slope of the line perpendicular to this line has the opposite reciprocal slope. To find the opposite reciprocal of 5/4, we must make it negative and switch the numerator and the denominator. The opposite reciprocal of 5/4 is -4/5.
Now, we must use this slope and the point we were given, (-5, 4), to write a new equation.
y = m(x-h) + k
y = -4/5(x + 5) + 4
y = -4/5x - 4 + 4
y = -4/5x
Therefore, your answer is y = -4/5x.
Hope this helps!