What is an equation of the line that passes through the point (-4,-7) and is perpendicular to the line x+2y=4 Answer Attempt 1 out of 2 square

## Step 1The given line is . We can rewrite this in slope-intercept form , where is the slope and is the y-intercept. ### can be rewritten as So, the slope of the given line is .## Step 2The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. ### The negative reciprocal of is .So, the slope of the line perpendicular to the given line is .## Step 3We know that the line passes through the point \((-4,-7)\). We can use the point-slope form of a line equation, \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and is the slope.### Substituting and \((x_1, y_1) = (-4,-7)\) into the equation, we get \(y - (-7) = 2(x - (-4))\).## Step 4Simplify the equation to get the final equation of the line.### \(y + 7 = 2(x + 4)\) simplifies to .