Final answer:
To find the slope-intercept form of the line perpendicular to 2x + 5y = 15, we first find the slope of the original line, which is -2/5, and then use the negative reciprocal for the new line. Using point (5,6), we solve for the y-intercept. However, the correct equation y = (5/2)x - 6.5 does not match any of the options provided, indicating a possible error.
Step-by-step explanation:
To find the slope-intercept form of a line that is perpendicular to another line, we first need to identify the slope of the original line. For the equation 2x + 5y = 15, rearrange it to slope-intercept form (y = mx + b) to find its slope, m.
2x + 5y = 15
5y = -2x + 15
y = -({2}/{5})x + 3
The slope of this line is -2/5. Because we want a line that is perpendicular to this one, its slope will be the negative reciprocal of -2/5. This means the slope of the new line is 5/2.
Now, we use the point (5,6) to find the y-intercept, b, of the new line:
y = mx + b
6 = (5/2)(5) + b
6 = 12.5 + b
b = 6 - 12.5 = -6.5
So the equation of the line in slope-intercept form is:
y = (5/2)x - 6.5
Looking at the answer choices, none of them match this equation. Therefore, there may be an error in either the question or the answer choices provided.