Answer
$y$ = 2$x$ - 2
Work Step by Step
We are finding the equation for a line using the point (3, 4) perpendicular to the line 2$x$ + 4$y$ = 5
First we put the line in slope-intercept form:
$y$ = -$\frac{1}{2}$$x$ + $\frac{5}{2}$
[To get to this equation: First subtract 2$x$ from both sides of the equation; Then divide both sides by 4. This leaves $y$ alone on the left side of the equation. The slope of $\frac{2}{4}$ is reduced to $\frac{1}{2}$, since both integers are divisible by 2.]
For perpendicular lines we take the inverse of the slope, so the lines will intersect (unlike in parallel lines where the slope is the same). The slope for the inverse line is 2$x$
Solving for the perpendicular line is similar to solving for a parallel line, using point-slope form:
$y$ - $y_{1}$ = $m$($x$ - $x_{1}$)
$y$ - 4 = 2($x$ - 3) *include the point (3, 4) and the slope
$y$ - 4 = 2$x$ -6 *distribute
$y$ = 2$x$ -2 *combine like terms
