Final answer:
The slope-intercept form of the equation for a line going through the point (5, 1) with a slope of -2/5 is y = -2/5x + 3. None of the provided options are correct as they do not have the right y-intercept, which should be 3.
Step-by-step explanation:
The question involves writing the slope-intercept form of the equation of a line that goes through a specific point with a given slope. The slope-intercept form is commonly represented as y = mx + b, where m is the slope and b is the y-intercept. Given the point (5, 1) and the slope -2/5, we can plug these values into the slope-intercept form to find the y-intercept.
The equation starts with y = -2/5x + b. To find b, we can substitute the x and y values from the point (5, 1) into the equation to get 1 = -2/5(5) + b. Simplifying, we get 1 = -2 + b, which leads to b = 3. Therefore, the correct equation is y = -2/5x + 3.
However, this correct option is not presented among the choices provided in the question. The closest option is c) y = -2/5x + 1, but it is incorrect because it does not have the right y-intercept.