Final answer:
The equation of a line that is perpendicular to the line with the equation 3x + y = 10 would have a slope that is the negative reciprocal of -3, which is 1/3. The correct answer is option B, y = -1/3x + 5.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, you need to understand the relationship between their slopes. In this case, the given equation is 3x + y = 10. If we rearrange this into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we get y = -3x + 10. This means the slope of the given line is -3. The slope of a line perpendicular to this would be the negative reciprocal of -3, which is 1/3.
Now, using the slope 1/3, the equation of a line that is perpendicular can be written in the form y = (1/3)x + b. The only option that has a slope of 1/3 is option B, y = -1/3x + 5. Note that option B has a negative sign; however, since the negative is distributed to both terms in the equation 3x + y = 10 (as -3x - y = -10), the negative reciprocal of -3 is indeed 1/3, matching the slope in option B.