Find the equation of the line parallel to 3x – 6y = 5 and passing through (-2, -3). Write the equation in slope-intercept form.

To find the equation of the line parallel to {eq}3x - 6y = 5 {/eq}, we need to find the slope of the given line. We can do this by solving the equation for y: {eq}3x - 6y = 5 {/eq} {eq}-6y = -3x + 5 {/eq} {eq}y = \frac{1}{2}x - \frac{5}{6} {/eq} So the slope of the given line is {eq}frac{1}{2}{/eq}. Since the line we're looking for is parallel, it will have the same slope. Now we can use the point-slope form of the equation of a line to find the equation of the line passing through {eq}(-2,-3){/eq} with slope {eq}frac{1}{2}{/eq}: {eq}y - y_1 = m(x - x_1) {/eq} where {eq}m = \frac{1}{2}{/eq}, {eq}x_1 = -2{/eq}, and {eq}y_1 = -3{/eq}. Plugging in the values, we get: {eq}y - (-3) = \frac{1}{2}(x - (-2)) {/eq} Simplifying: {eq}y + 3 = \frac{1}{2}x + 1 {/eq} {eq}y = \frac{1}{2}x - 2 {/eq} So the equation of the line parallel to {eq}3x - 6y = 5 {/eq} and passing through {eq}(-2,-3){/eq} is {eq}y = \frac{1}{2}x - 2.{/eq}