Final answer:
The gradient of the line represented by the equation y - 4 = 3x is found by rewriting the equation in slope-intercept form to get y = 3x + 4, where the gradient (m) is the coefficient of x, which is 3.
Step-by-step explanation:
The gradient of a line, often denoted by m, indicates the steepness of the line. The student's question asks to work out the gradient for the equation y - 4 = 3x. To find the gradient, we can rewrite the equation in the slope-intercept form, which is y = mx + b, where m is the gradient and b is the y-intercept.
Adding 4 to both sides of the equation we get y = 3x + 4. In this form, it is clear that the coefficient of x (which is 3) is the gradient of the line. Therefore, the gradient is 3.
This aligns with the concept that the gradient of a line is calculated by dividing the change in the y-value by the change in the x-value, which in this case, is explicitly given as 3 in front of the x in the equation.