Final answer:
The standard form of the equation of the line passing through (-2,-3) and (2,-5) is 2x - y = 4.
Step-by-step explanation:
To find the standard form of the equation of a line, we need to determine the values of A, B, and C in the equation Ax + By = C. We can do this by using the given points (-2,-3) and (2,-5).
Step 1: Find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). In this case, the slope is (-5 - (-3)) / (2 - (-2)) = -2/4 = -1/2.
Step 2: Use the slope-intercept form of the equation y = mx + b to find the y-intercept (b). Using one of the given points, (-2,-3), we can substitute the coordinates into the equation to find b. -3 = (-1/2)(-2) + b. Solving for b, we get b = -2.
Step 3: Substitute the slope (m) and y-intercept (b) into the standard form equation Ax + By = C. Plugging in the values, we have -1/2x + y = -2.
Step 4: Multiply both sides of the equation by 2 to get rid of the fraction, and rearrange to put the equation in standard form. The final answer is 2x - y = 4.