I am stuck on this problem for a while now, can anybody please help.

Question

Write an equation of the line that passes through (0, 6) and is parallel to y=5x−3.

Answer 1

y = mx + b where m is the slope and b is the y-intercept, Your equation is y = 5x - 3, so the slope is 5 and the y-intercept is -3. Parallel lines have the same slope, so the slope of the parallel line is also 5:

y = 5x + b

Now we just need to find the y-intercept (b). By definition, the y-intercept crosses the y-axis, so the x-value of the y-intercept is 0. The point you are given is (0,6), so the y-intercept is 6.

y = 5x + 6