Determine the equation of a straight-line that passes through two points (4;4)(4;4) and (−2;−2)(−2;−2). A.y=x−4𝑦=𝑥−4B.y=x+8𝑦=𝑥+8C.y=−x−4𝑦=−𝑥−4D.y=x

The equation of a straight line passing through two points (x1, y1) and (x2, y2) can be found using the formula for the slope (m) of a line: m = (y2 - y1) / (x2 - x1).

Step 1: Identify the coordinates of the two points. In this case, the points are (4,4) and (-2,-2).

Step 2: Substitute the coordinates of the points into the formula for the slope. This gives: m = (-2 - 4) / (-2 - 4) = 1.

Step 3: The equation of a line is y = mx + c, where m is the slope and c is the y-intercept. Since the slope is 1, the equation becomes y = x + c.

Step 4: To find the y-intercept (c), substitute one of the points into the equation. If we use the point (4,4), we get 4 = 4 + c. Solving for c gives c = 0.

Step 5: Substitute c = 0 back into the equation to get the final equation of the line: y = x.

So, the correct answer is D. y = x.