Final answer:
The equation of the line passing through (4, -6) with a slope of -5/2 is found using the point-slope form and simplifying to obtain the final equation in slope-intercept form, giving y = -5/2x + 4.
Step-by-step explanation:
The equation of the line that passes through the point (4, -6) and has a slope of -5/2 can be found using the point-slope form of a linear equation, which is y - y1 = m(x - x1). Here, (x1, y1) is the point the line passes through and m is the slope of the line.
In this case, we have the point (4, -6) and the slope m = -5/2. Substituting these values into the point-slope form gives us:
y - (-6) = -5/2(x - 4)
Simplifying this equation, we get:
y + 6 = -5/2(x - 4)
Distributing the slope on the right side:
y + 6 = -5/2x + 10
Finally, subtracting 6 from both sides to get the y-intercept form y = mx + b, we have:
y = -5/2x + 4