Final answer:
The equation of the line that is perpendicular to y=4x+8 and has a y-intercept of 3 is y=-1/4x+3, using the negative reciprocal rule for perpendicular slopes.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line and has a specific y-intercept, we need to understand the properties of perpendicular lines and how they relate to slope. The given line has an equation y = 4x - 3 + 11, which simplifies to y = 4x + 8. Since perpendicular lines have slopes that are negative reciprocals of each other, we can deduce that the slope of the line we are looking for is -1/4 (the negative reciprocal of 4).
The fact that the new line has a y-intercept of 3 means that when x = 0, y = 3. Incorporating this information, the equation for our new line is y = -1/4x + 3. Hence, this is the equation of the line that is perpendicular to the given line and has the required y-intercept.