# How do you write an equation (a) in slope intercept form and (b) in standard form for the line passing through (1,8) and perpendicular to 2x+5y=1?

Dec 15, 2016

#### Explanation:

To make any line that is perpendicular to a line in standard form:

$a x + b y = c$

Swap "a" and "b" and, if "b" was negative then make it positive, otherwise, change the sign of "a". Therefore, a line that is perpendicular to:

$2 x + 5 y = 1$

Will have the form:

$5 x - 2 y = c$

To make it pass through the point $\left(1 , 8\right)$, substitute the point into the above and then solve for c:

$5 \left(1\right) - 2 \left(8\right) = c$

$c = - 11$

The standard form is

$5 x - 2 y = - 11$

The slope intercept form is

$y = \frac{5}{2} x + \frac{11}{2}$