Question

05.01 MC)

Determine the equation of the line with slope −2 that passes through the point M(−1, −3). (5 points)

Question 2 options:

1)

2x + y = −5

2)

2x − y = −5

3)

x − 2y = 5

4)

x − 2y = −5

Answer 1

2x + y = -5 (which is Answer 1).

Explanation:

The possible answer choices are all versions of the standard equation of a straight line: Ax + By + C = 0. If A and B are both positive, as they are here, then the slope is negative and has the form m = -A/B. Only the first answer choice passes here: with +2x and +1y, the slope is -2. This automatically eliminates the other possibilities.

Looking at the first answer choice, we see that A must be 2 and B must be 1

so that the slope is m = -2. Writing out this equation: Ax + By + C = 0.

Replace A with 2 and B with 1: 2x + y + C = 0.

Finally, replace x with -1 and y with -3: 2(-1) + (-3) + C = 0.

Solving this for C, we get -2 - 3 + C = 0, or -5 + C = 0, or C = 5.

We end up with 2x + y = -5 (which is Answer 1).