Write an equation for a line perpendicular to $$ y=-2 x+5 $$ and passing through the point $$ (-2,2) $$ $$ y= $$ Question Help: Video Submit Question

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1. The slope of the given line $$ y = -2x + 5 $$ is $$-2$$.

2. For a line perpendicular to this line, its slope $$ m $$ is the negative reciprocal of $$-2$$:
   $$
   m = -\frac{1}{-2} = \frac{1}{2}
   $$

3. Use the point-slope form of the equation with the point $$(-2, 2)$$ and slope $$ \frac{1}{2} $$:
   $$
   y - 2 = \frac{1}{2}(x - (-2)) = \frac{1}{2}(x + 2)
   $$

4. Solve for $$ y $$:
   $$
   y - 2 = \frac{1}{2}x + 1
   $$
   $$
   y = \frac{1}{2}x + 1 + 2
   $$
   $$
   y = \frac{1}{2}x + 3
   $$

Thus, the equation of the line is:
$$
y = \frac{1}{2}x + 3
$$
The equation of the line perpendicular to $$ y = -2x + 5 $$ and passing through the point $$(-2, 2)$$ is: $$ y = \frac{1}{2}x + 3 $$

Write an equation for a line perpendicular to \( y=-2 x+5 \) and passing through the point \( (-2,2) \) \( y= \) Question Help: Video Submit Question

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