Determine the equation of the line between the coordinates: (-2,-5) and (-4,-2)

To find the equation of the line passing through the coordinates (-2, -5) and (-4, -2), we'll use the point-slope form of a linear equation: $$ y-y_1=\:m\left(x-x_1\right) $$ Given the points, we can calculate the slope m: $$ m=\frac{y_2-y_1}{x_2-x_1} $$ $$ m=\frac{-2-(-5)}{-4-\left(-2\right)}=\frac{3}{-2}=\:-\frac{3}{2} $$ Now, we can choose either point to plug into the point-slope form. Let's use (−2,−5) as the point: y-(-5) = -3/2 (x -(-2)), y + 5 = -3/2 (x + 2) Now, let's distribute the slope: y + 5 = -3/2x - 3 Subtract 5 from both sides: y = -3/2x - 3 - 5 y = -3/2x - 8 So, the equation of the line passing through the coordinates (-2, -5) and (-4, -2) is: y = -3/2x - 8