To find the equation of a line passing through two points, (-1, -5) and (5, 4), we can use the point-slope form of a linear equation.
The formula for the point-slope form is: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.
First, let's calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1, -5) and (x2, y2) = (5, 4).
m = (4 - (-5)) / (5 - (-1))
m = 9 / 6
m = 3/2
Now, we can choose one of the points, let's use (-1, -5), and substitute the values into the point-slope form:
y - y1 = m(x - x1)
y - (-5) = (3/2)(x - (-1))
y + 5 = (3/2)(x + 1)
To convert this equation to the standard form (Ax + By = C), we can multiply through by 2 to eliminate the fraction:
2(y + 5) = 3(x + 1)
2y + 10 = 3x + 3
3x - 2y = 7
So, the equation of the line passing through the points (-1, -5) and (5, 4) is 3x - 2y = 7.