Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form Passing through \( (8,6) \) with \( x \)-intercept -4 Write an equation for the line in point-slope form (Simplify your answer Use integers or fractions for any numbers in the equation )

To find the equation of the line, we first need to determine the slope using the given points. The x-intercept is where \(y = 0\), and from the problem, we know the x-intercept is -4. So, the two points we have are \( (8, 6) \) and \( (-4, 0) \). The slope \(m\) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 6}{-4 - 8} = \frac{-6}{-12} = \frac{1}{2} \] Now, using the point-slope form \(y - y_1 = m(x - x_1)\) with point \( (8,6) \): \[ y - 6 = \frac{1}{2}(x - 8) \] This is the equation in point-slope form. To convert this to slope-intercept form \(y = mx + b\), we simplify: \[ y - 6 = \frac{1}{2}x - 4 \] \[ y = \frac{1}{2}x + 2 \] So, the equation of the line in point-slope form is: \(y - 6 = \frac{1}{2}(x - 8)\) And in slope-intercept form, it's: \(y = \frac{1}{2}x + 2\)