Linear Light works almost exactly like Vivid Light except that it lightens or darkens by increasing or decreasing brightness instead of contrast. If the blend color is more than 50% brightness the image is dodged (lightened) by increasing the brightness. If the blend color is less than 50% brightness, the image is burned (darkened) by decreasing the brightness. Like all the "Light" blending modes, 50% gray has no effect on the image.
Linear light can be used for tonal and color in much the same was as Vivid Light, it just gives a slightly different result and can be used to add a boost of color into images where there is little contrast. And, like most blending modes, it can be used for image effects as shown in this tutorial for a stylized photo effect.
