Final answer:
The equation of the line in slope-intercept form that crosses the x-axis at 6 and is perpendicular to y = -x + 9 is y = x - 6, which is not listed in the given options. Therefore, there is likely a typo in the question or the answer choices.
Step-by-step explanation:
The student is asking for the equation of a line in slope-intercept form that crosses the x-axis at 6 and is perpendicular to the line given by y = -x + 9. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Since the line we want is perpendicular to y = -x + 9, which has a slope of -1, the slope of the desired line will be the negative reciprocal of -1, which is 1. Thus, the slope (m) of the new line will be 1. To find the y-intercept (b), we use the fact that the line crosses the x-axis at 6 (this means when y=0, x=6). Substituting these values into the slope-intercept form:
- y = (1)x + b
- 0 = (1)(6) + b
- b = -6
So the equation of the line is y = x - 6, which is not present in the options given. There may be a typo in one of the options, as y = x - 6 should be included. Based on the given options, none are correct as none represent a line with a slope of 1 and a y-intercept of -6.