Question

Write an equation of the line that passes through the point (0, 3) and

parallel to y = 4x - 2.
A. y = 4x + 3
B. y = 4x - 2
C. y = -1/4x + 3
D. y = -1/4x - 2

Answer 1

The equation of the line parallel to y = 4x - 2 and passing through the point (0, 3) is y = 4x + 3.

Step-by-step explanation:

To find the equation of a line parallel to y = 4x - 2 and passing through the point (0, 3), we need to note that parallel lines have the same slope. So, the slope of the line we're looking for is also 4. Using the point-slope form of a linear equation, we can write the equation as y - y1 = m(x - x1). Substituting the values, we get y - 3 = 4(x - 0). Simplifying, we have y - 3 = 4x. Adding 3 to both sides gives us y = 4x + 3. Therefore, the equation of the line parallel to y = 4x - 2 and passing through the point (0, 3) is y = 4x + 3 (Option A).