Identify an equation in point-slope form for the line perpendicular to y=-2x+8 that passes through (-3,9) A. y-9=(1)/(2)(x+3) B. y+3=(1)/(2)(x-9) C. y+9=2(x-3)fv D. y-9=-2(x+3)

To find the equation of a line perpendicular to $y=-2x+8$ that passes through $(-3,9)$, we need to determine the slope of the perpendicular line.<br /><br />The slope of the given line $y=-2x+8$ is $-2$. The slope of a line perpendicular to this line is the negative reciprocal of $-2$, which is $\frac{1}{2}$.<br /><br />Now, we can use the point-slope form of a line equation, which is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.<br /><br />Substituting the values, we have:<br />$y - 9 = \frac{1}{2}(x - (-3))$<br /><br />Simplifying the equation, we get:<br />$y - 9 = \frac{1}{2}(x + 3)$<br /><br />Therefore, the equation in point-slope form for the line perpendicular to $y=-2x+8$ that passes through $(-3,9)$ is:<br />A. $y-9=\frac {1}{2}(x+3)$