Final answer:
The equation of the line parallel to y=2x+5 that passes through the point (2, 8) is y = 2x + 4. This is found by using the same slope as the original line (slope of 2) and the coordinates of the given point to solve for the y-intercept.
Step-by-step explanation:
The student is asking for an equation of a line that is parallel to the given line y=2x+5 and passes through a specific point (2, 8). To find the equation of a parallel line, we need to use the same slope as the original line because parallel lines have the same slope.
The equation of a line is generally written as y = mx + b, where m is the slope and b is the y-intercept. Since the slope of the given line is 2 (from the equation y=2x+5), the slope of the parallel line will also be 2.
We have the point (2, 8) through which the new line must pass. By plugging the x and y values of this point into the equation, along with the slope, we can solve for b, the y-intercept.
Substituting into the equation gives us:
8 = 2(2) + b
8 = 4 + b
4 = b
Therefore, the equation of the line that is parallel to y=2x+5 and passes through the point (2, 8) is y = 2x + 4.