find the equation of the line in all 3 forms- point slope, slope intercept and standard

Question

perpendicular to -2x+5y=1, through (-5,0)

Answer 1

-2x +5y = 1

solve for y

5y =2x +1

divide by 5

y = 2x/5 +1/4

the slope = 2/5, the coefficient of the x term when the equation is solved for y

a perpendicular line will have a negative inverse slope. change the sign and flip 2/5 upside down to get -5/2

y = -5x/2 + b, plug in the point (-5,0) to solve for b, the y intercept

0 = -5(-5)/2 + b

b =-25/2

y=-5x/2 - 25/2 is the perpendicular line through the given point in slope intercept form

slope = (y-0)/(x+5) = -5/2

is in point slope form

5x +2y +25 =0 is in standard ax+by + c = 0 form