Line g has an equation of y=2x+1 Line h includes the point (-5,2) and is perpendicular to line g. What is the equation of line h? Write the equation in slope-intercept form . Write the numbers in the equation as simplified proper fractions , improper fractions , or integers. square

To find the equation of line h, we need to determine its slope and use the point-slope form of a linear equation.<br /><br />Step 1: Find the slope of line g.<br />The slope of line g is given by the coefficient of x in the equation y = 2x + 1. Therefore, the slope of line g is 2.<br /><br />Step 2: Find the slope of line h.<br />Since line h is perpendicular to line g, its slope is the negative reciprocal of the slope of line g. Therefore, the slope of line h is -1/2.<br /><br />Step 3: Use the point-slope form to write the equation of line h.<br />The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.<br /><br />Using the point (-5, 2) and the slope -1/2, we can substitute these values into the point-slope form:<br />y - 2 = -1/2(x - (-5))<br /><br />Simplifying this equation, we get:<br />y - 2 = -1/2(x + 5)<br /><br />Step 4: Convert the equation to slope-intercept form.<br />To convert the equation to slope-intercept form, we need to solve for y:<br />y = -1/2(x + 5) + 2<br /><br />Expanding and simplifying, we get:<br />y = -1/2x - 5/2 + 2<br /><br />Combining like terms, we get:<br />y = -1/2x - 1/2<br /><br />Therefore, the equation of line h in slope-intercept form is:<br />y = -1/2x - 1/2