Final answer:
The equation of the line in slope-intercept form, given that it passes through the point (6,3) and has a slope of -5/2, is
y = (-5/2)x + 18.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, which is y = mx + b, we need to know the slope (m) and the y-intercept (b).
Given that the line passes through the point (6,3) and has a slope of -5/2, we can use the point-slope formula to find the equation of the line:
y - y1 = m(x - x1)
Substituting in the point (6,3) and the slope -5/2, we have:
y - 3 = (-5/2)(x - 6)
Distributing the slope on the right side gives us:
y - 3 = (-5/2)x + 15
Adding 3 to both sides to solve for y, we obtain the slope-intercept form of the equation:
y = (-5/2)x + 18