Final answer:
To find the slope-intercept form of a line perpendicular to -2x + 5y = -10 and passing through (2, -3), first determine the slope of the original line, then find the negative reciprocal to get the perpendicular slope, and lastly use the point to solve for the y-intercept.
Step-by-step explanation:
To write the equation in slope-intercept form (y = mx + b), where the line is perpendicular to another and passes through a specific point, the first step is to find the slope of the original line. The given equation, -2x + 5y = -10, can be rearranged to solve for y and find its slope. Rearranging, we get 5y = 2x - 10, so y = (2/5)x - 2. The slope of this line is 2/5, and hence, the slope of the perpendicular line will be the negative reciprocal, which is -5/2.
With the slope m = -5/2 and using the point (2, -3), we can substitute these into the slope-intercept form to find b. Plug in the point: -3 = (-5/2)(2) + b, which simplifies to -3 = -5 + b, so b = 2.
Finally, the equation of the line in slope-intercept form is y = (-5/2)x + 2.