Final answer:
To find the equation of the line parallel to y = 4x – 2 that passes through the point (-1,5), we need to use the fact that parallel lines have the same slope. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Using the point-slope form of the equation, we substitute the given slope and point into the equation and simplify to find the equation of the parallel line.
Step-by-step explanation:
To find the equation of the line parallel to y = 4x – 2 that passes through the point (-1,5), we need to use the fact that parallel lines have the same slope. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the given line has a slope of 4, the parallel line will also have a slope of 4.
Using the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the given point, we substitute m = 4 and (x1, y1) = (-1, 5) into the equation. Simplifying, we get y - 5 = 4(x + 1). Expanding and rearranging, the equation becomes y = 4x + 9.