Final answer:
To determine the equation of a line parallel to y=5x+2 that passes through the point (-2,1), we can use the point-slope form and plug in the point and the slope to find the equation of the line: y = 5x + 11.
Step-by-step explanation:
To determine the equation of a line parallel to y=5x+2 that passes through the point (-2,1), we need to use the fact that parallel lines have the same slope.
The given line has a slope of 5, so the parallel line will also have a slope of 5.
Using the point-slope form, we can plug in the point and the slope to find the equation of the line:
y - y1 = m(x - x1)
y - 1 = 5(x + 2)
Rearranging the equation in slope-intercept form:
y = 5x + 11