Final answer:
The equation of the line with a slope of -1/3 passing through point (-3, 8) is y = -1/3x + 7, matching option (b). To derive this, the slope and point are substituted into the slope-intercept form and simplified to find the y-intercept.
Step-by-step explanation:
The student is asking for the equation of a straight line in slope-intercept form (y = mx + b) with a given slope of -1/3 that passes through a specific point (-3, 8). To find the equation, we can plug the slope and the coordinates of the point into the slope-intercept form.
Using the point (-3, 8), the equation becomes y - 8 = -1/3(x + 3). Simplifying this equation will give us the y-intercept (b).
Solving step-by-step:
- y - 8 = -1/3x - 1
- y = -1/3x - 1 + 8
- y = -1/3x + 7
The correct equation, therefore, is y = -1/3x + 7, which matches option (b).