Which is an equation of a line that passes through the point (5,4)And is perpendicular to the line shown. Start in point-slope form: ,Change to slope intercept form:

you find that lines slope with points (4,1)and (0,4) so you do 4-0=4 ad 1-4=-3 so the slope is -3/4 for the line shown so the line we needs slope will be the opposite recipricole so 4/3 and to get the equation you have to plug everything in first 4=(4/3)5+b so that we can find b ( the y intercept)
4=6 2/3 +b
2 1/3=b
the equation is y=4/3+2 1/3