Question

Write the equation of the line through the

points (-12, 14) and (6, -1) in POINT-SLOPE
FORM.

Option 1: y = -1/18x - 5/3
Option 2: y = -1/18x + 5/3
Option 3: y = 18x - 5/3
Option 4: y = 18x + 5/3

Answer 1

To find the equation in point-slope form for the line passing through (-12, 14) and (6, -1), we calculate the slope as -5/6 and apply it using one of the points. The resulting equation is y - 14 = (-5/6)(x + 12). None of the provided options are correct.

Step-by-step explanation:

To write the equation of the line through the points (-12, 14) and (6, -1) in point-slope form, first we must calculate the slope of the line. The slope is calculated as the change in y divided by the change in x (rise over run). Using the provided points:

• Slope (m) = (y2 - y1) / (x2 - x1)

• Slope (m) = (-1 - 14) / (6 - (-12))

• Slope (m) = (-15) / (18)

• Slope (m) = -5/6

Now, we use one of the points and the slope to write the equation in point-slope form (y - y1) = m(x - x1). Let's use the point (-12, 14):

• y - 14 = (-5/6)(x - (-12))

• y - 14 = (-5/6)(x + 12)

This gives us the equation of the line in point-slope form. None of the given options matches this equation, indicating a possible error in the provided options or in the question itself.