The general equation of a line in slope-intercept form is y = ax + b. In this equation the variable "a" (the variable in front of "x") represents the slope of the line.
Since our new line is parallel to y = 5x + 3, both lines will have the same slope. Therefore we can already conclude that our line has the equation y = 5x + b.
To find the value of our variable "b", we must plug in the x- and y-coordinate of the point that is on the line. We get the following:
14 = 5*(4) + b Multiply
14 = 20 + b Subtract 20.
-6 = b Eventually switch sides
b = -6 Hence, the equation of the line in slope-intercept form is y = 5x - 6
