Answer:
y= -5x+8
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.
Let's rewrite the formula of the given line so it is in the form of y=mx+c, to find out its gradient.
5y-x=20
5y= x+20
[tex]y = \frac{1}{5} x + 4[/tex] (÷5 throughout)
Hence, the gradient of the given line is [tex] \frac{1}{5} [/tex].
The product of the gradients of 2 perpendicular lines is-1.
[tex] \frac{1}{5} (gradient \: of \: line) = - 1 \\ gradient \: of \: line = - 1 \div \frac{1}{5} \\ gradient \: of \: line = - 5[/tex]
Subst. m= -5 into the equation.
y= -5x +c
To find c, substitute a coordinate into the equation.
When x=2, y= -2,
-2 = -5(2) +c
-2= -10 +c
c= 10 -2
c= 8
Thus, the equation of the line is y= -5x +8.
