Final answer:
The equation of the line that is perpendicular to y = −x + 8 and has an x-intercept of 6 is y = x - 6.
Step-by-step explanation:
The question is asking for the equation of a line that is perpendicular to the line represented by y = -x + 8 and that intersects the x-axis at (6,0). To find a perpendicular line, we need to identify the negative reciprocal of the original line's slope. If the slope of the original line is -1 (as in y = -1x + 8), the slope of the perpendicular line will be the negative reciprocal, which is 1 (positive one). Therefore, the perpendicular line will have the form y = x + b. To determine b, we use the fact that this line has an x-intercept at 6. This means that when x = 6, y = 0; hence, we can write 0 = 6 + b, leading to b = -6.
The equation of the perpendicular line is y = x - 6, which matches option (b).