Final answer:
The equation of the line in slope-intercept form with a slope of 1/3 that passes through (-5, 2) is y = 1/3x + 11/3.
Step-by-step explanation:
The student is asking for the equation in slope-intercept form of a line that has a slope of ⅓ and passes through the point (-5, 2). To find the slope-intercept form, which is y = mx + b, we substitute the given slope (m) and the coordinates of the given point into the equation to solve for the y-intercept (b). In this case, we plug in 1/3 for m, -5 for x, and 2 for y, which gives us 2 = (1/3)(-5) + b. Solving for b, we get 2 + 5/3 = b, or b = 11/3. Therefore, the slope-intercept form of the equation is y = ⅓x + ⅓³.