Final answer:
The equation in point-slope form of the line passing through (-7, 1) and (-3, 9) is D. y - 9 = 2(x + 3), obtained by first calculating the slope and then applying the point-slope formula using one of the given points.Option D is the correct answer.
Step-by-step explanation:
The question asks us to find the equation, in point-slope form, of the line that passes through the points (-7, 1) and (-3, 9). To do this, we first need to calculate the slope of the line using the two given points.
We use the slope formula: slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points in, we get:
m = (9 - 1) / (-3 + 7) = 8 / 4 = 2.
Now, with the slope determined and one of the points, we can write the equation of the line in point-slope form, which is y - y1 = m(x - x1). Using the point (-7, 1) and the slope 2, the point-slope form is:
y - 1 = 2(x + 7).
None of the options exactly matches this form, but we can manipulate our equation to match one of the given options. By distributing the slope and moving '1' to the other side, our equation becomes:
y - 9 = 2(x + 3), which corresponds to Option D.