Answer:
5x + y = 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange x - 5y = 10 into this form
Subtract x from both sides
- 5y = - x + 10 ( divide all terms by - 5 )
y = [tex]\frac{1}{5}[/tex] x - 2 ← in point- slope form
with m = [tex]\frac{1}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m\\}[/tex] = - [tex]\frac{1}{\frac{1}{5} }[/tex] = - 5, thus
y = - 5x + c ← is the partial equation of the line
To find c substitute (1, 2) into the partial equation
2 = - 5 + c ⇒ c = 2 + 5 = 7
y = - 5x + 7 ← in slope - intercept form
Add 5x to both sides
5x + y = 7 ← in standard form
