Question

Identify the equation of a line that passes through (-1, 1) and (-2, 13).

A) y = -12x - 11
B) y = -11x - 12
C) y = -13x - 10
D) y = -10x - 13

Answer 1

The equation of the line that passes through (-1, 1) and (-2, 13) is calculated by finding the slope and using the point-slope form. The resulting equation is y = -12x - 11, which is option A.

Step-by-step explanation:

To identify the equation of the line that passes through the points (-1, 1) and (-2, 13), we start by calculating the slope (m) of the line using the slope formula m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula: m = (13 - 1) / (-2 + 1) = 12 / -1 = -12.

Now that we have the slope, we can use one of the points and the slope to write the equation of the line in point-slope form, y - y1 = m(x - x1), and then convert it to slope-intercept form, y = mx + b.

Using the point (-1, 1), we get y - 1 = -12(x + 1). Expand this to get y - 1 = -12x - 12. Adding 1 to both sides, we obtain y = -12x - 11. Therefore, the equation of the line is y = -12x - 11, which corresponds to choice A.