Final answer:
The correct equation for the tangent line is in the slope-intercept form y = mx + b, where m is the slope, found by taking the derivative of the function at the point, and b is the y-intercept. Therefore, the mcq answer in the final answer is: d) y = mx + b.
Step-by-step explanation:
The student is asking for the equation of a tangent line, which can be represented in slope-intercept form. In most algebra courses, this is taught as y = mx + b, where m is the slope of the tangent line and b is the y-intercept. To find the equation of a line tangent to a function at a particular point, you would first need to calculate the slope of the tangent line, which is the derivative of the function (f'(x)) at that point. Then you would use the point-slope form ({y - y1} = m({x - x1}), where (x1, y1) is the point of tangency, and rearrange to slope-intercept form if necessary.
Given the four multiple-choice options, the correct equation for a tangent line is typically expressed as y = mx + b, where m is the derivative of the function at the point of tangency, representing the slope of the tangent, and b is the y-intercept of the tangent line. The other options provided do not correctly represent the standard equation of a tangent line.