Please help! Thanks!

Question

What is the slope of a line that is perpendicular to the graph of 5x+4y=7?

a. -5/4

b. 5/4

c. -4/5

d. 4/5

Answer 1

d. 4/5

5x +4y = 7

solve for y

subtract 5x from both sides

4y =-5x +7

divide both sides by 4

y = (-5/4)x + 7/4

the coefficient of the x term, when the equation is solved for y, is the slope

the slope =-5/4

the perpendicular line has slope = the negative inverse. take -5/4, change the sign and flip the fraction upside down to get +4/5. That's the slope of the perpendicular line