4) The equation for line a can be written as y-8=-2(x-4) Line h is parallel to line o and passes through (-5,1) What is the equation of line h?

To find the equation of line h, we need to use the point-slope form of a linear equation, which is given by:<br /><br />$y - y_1 = m(x - x_1)$<br /><br />where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.<br /><br />Since line h is parallel to line o, it will have the same slope as line o. We can find the slope of line o by rearranging the equation for line a:<br /><br />$y - 8 = -2(x - 4)$<br /><br />Simplifying this equation, we get:<br /><br />$y = -2x + 16 + 8$<br /><br />$y = -2x + 24$<br /><br />From this equation, we can see that the slope of line o is -2. Therefore, the slope of line h is also -2.<br /><br />Now, we can substitute the values of the point $(-5, 1)$ and the slope -2 into the point-slope form of the equation:<br /><br />$y - 1 = -2(x - (-5))$<br /><br />Simplifying this equation, we get:<br /><br />$y - 1 = -2(x + 5)$<br /><br />Expanding and rearranging the equation, we get:<br /><br />$y - 1 = -2x - 10$<br /><br />Adding 1 to both sides of the equation, we get:<br /><br />$y = -2x - 9$<br /><br />Therefore, the equation of line h is $y = -2x - 9$.