Final answer:
To find an equation that is parallel to y = 1/4x + 2 and passes through the point (4, 12), we need to find the slope of the given equation, since parallel lines have the same slope. The slope of the given equation is 1/4. Using the point-slope form, we can substitute the slope and coordinates into the equation to find the equation of the parallel line: y = (1/4)x + 11.
Step-by-step explanation:
To find an equation that is parallel to y = 1/4x + 2 and passes through the point (4, 12), we need to find the slope of the given equation, since parallel lines have the same slope.
The given equation is in the form y = mx + b, where m is the slope. In this case, the slope is 1/4.
Using the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point, we can substitute the slope and coordinates into the equation to find the equation of the parallel line:
y - 12 = (1/4)(x - 4)
Expanding and simplifying:
y - 12 = (1/4)x - 1
y = (1/4)x + 11
Therefore, the linear equation parallel to y = 1/4x + 2 and passing through the point (4, 12) is y = (1/4)x + 11.