Question

Arrange your answer in the form y = mx + b, where b is constant. The coordinates are (1,2), (-1,-2).

(a) y = x + 1
(b) y = x - 1
(c) y = -x + 1
(d) y = -x - 1

Answer 1

None of the given choices (a-d) correctly represents the line through the coordinates (1,2) and (-1,-2). The correct equation, calculated through the slope formula, should be y = 2x + 0, which is not listed among the options.

Step-by-step explanation:

To find which linear equation best represents the coordinates (1,2) and (-1,-2), we need to determine the slope (m) and y-intercept (b) of the line that passes through these points. To calculate the slope, we use the formula m = (y2 - y1) / (x2 - x1). For the points given, that is (2 - (-2)) / (1 - (-1)) = 4/2 = 2. Now we know the slope (m) is 2.

Next, we can use either point to find the y-intercept (b). Let's use the point (1,2) and the formula of the line y = mx + b. We substitute the x and y values to get 2 = (2)(1) + b, which gives us b = 0. Thus, the equation representing this line is y = 2x.

However, since we must express the equation in the form y = mx + b, where b is a constant, we write it as y = 2x + 0. This means that the correct option that matches the slope and y-intercept is none of the given choices (a-d), as they all have a slope of either 1 or -1, whereas we need a slope of 2.