This quiz: 10 point(s) possible This question: 1 point(s) possible Find the equation of line $b$ described below, in slope-intercept form. Line $a$ is perpendicular to line $b$. Line a passes through the points $(1,-10)$ and $(9,-14)$. Line b passes through the point $(-6,-12)$. The equation of line $b$ is $y=$ (Simplify your answer. Type an expression using $x$ as the variable. Use integers or fractions any numbers in the expression.)

Step 1 ：Find the slope of line a using the formula: \(m_a = \frac{y_2 - y_1}{x_2 - x_1}\)

Step 2 ：\(m_a = \frac{-14 - (-10)}{9 - 1} = \frac{-4}{8} = -\frac{1}{2}\)

Step 3 ：Since line a and line b are perpendicular, their slopes are negative reciprocals: \(m_b = -\frac{1}{m_a}\)

Step 4 ：\(m_b = -\frac{1}{-\frac{1}{2}} = 2\)

Step 5 ：Use the point-slope form to find the equation of line b: \(y - y_1 = m_b(x - x_1)\)

Step 6 ：\(y - (-12) = 2(x - (-6))\)

Step 7 ：\(y + 12 = 2(x + 6)\)

Step 8 ：Solve for y to get the equation in slope-intercept form: \(y = 2x - 12\)

Step 9 ：\(\boxed{y = 2x - 12}\)