Final answer:
The equation in slope-intercept form of a line that crosses the x-axis at 36 and is perpendicular to the line y = -4/9x + 5 is y = 9/4x.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the line y = -4/9x + 5 and crosses the x-axis at 36, we need to determine the slope of the perpendicular line. The slope of the original line is -4/9, so the slope of the perpendicular line will be the negative reciprocal, which is 9/4.
Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. Since the line crosses the x-axis at 36, the y-intercept is 0. So the equation of the line is y = 9/4x + 0. However, we can simplify this to y = 9/4x.
Therefore, the correct equation in slope-intercept form is y = 9/4x.