Question

What is the equation in point-slope form of a line that passes through the following points: (-3, -1) and (6, 7)?

a) y - 7 = 8/9(x - 6)
b) y - 6 = 8/9(x - 7)
c) y - 6 = 2(x - 7)
d) y - 7 = 2(x - 6)

Answer 1

The equation in point-slope form of a line passing through the points (-3, -1) and (6, 7) is y + 1 = 8/9(x + 3).

Step-by-step explanation:

To find the equation of a line that passes through two points, we can use the point-slope form: y - y1 = m(x - x1). Where (x1, y1) are the coordinates of one of the points and m is the slope of the line.

Using the points (-3, -1) and (6, 7), we can calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (7 - (-1)) / (6 - (-3)) = 8/9.

Now, we can choose one of the points and substitute the values into the point-slope form. Let's use the point (-3, -1): y - (-1) = 8/9(x - (-3)). Simplifying this equation gives the answer: y + 1 = 8/9(x + 3).