Final answer:
The equation of the line passing through the points (4,-5) and (-2,6) is y = (-11/6)x + 7/3.
Step-by-step explanation:
To find the equation of the line that passes through the points (4,-5) and (-2,6), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
First, let's find the slope m:
m = (y2 - y1)/(x2 - x1)
Using the x and y values of the given points, we have:
m = (6 - (-5))/(-2 - 4) = 11/-6 = -11/6
Next, let's choose one of the points (4,-5) and substitute the values into the slope-intercept form to find the y-intercept b:
-5 = (-11/6)(4) + b
-5 = -44/6 + b
b = -5 + 44/6 = -30/6 + 44/6 = 14/6 = 7/3
Therefore, the equation of the line passing through the given points is y = (-11/6)x + 7/3.