Final answer:
Using the point-slope form of the equation of a line, the equation for a line passing through the point (4, 1/3) with a slope of 3/4 is derived to be y = 3/4x - 8/3. However, none of the provided options match this equation, indicating a possible typo in the options.
Step-by-step explanation:
To find the equation of a line that passes through a specific point and has a given slope, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes and m is the slope of the line.
Given the point (4, 1/3) and the slope 3/4, we can plug these values in to get the equation of the line:
y - 1/3 = 3/4(x - 4)
To find the equation in slope-intercept form, which is y = mx + b, we will simplify the above equation:
y - 1/3 = 3/4x - 3
Adding 1/3 to both sides gives us:
y = 3/4x - 3 + 1/3
Finding a common denominator and combining terms gives us:
y = 3/4x - 9/3 + 1/3
y = 3/4x - 8/3
Therefore, the equation that represents the line is:
y = 3/4x - 8/3
However, none of the options given in the student's question has this equation, there may be a typo in the options. The correct answer with the slope 3/4 and passing through the point (4, 1/3) is not listed.