Question

What is the equation in point-slope form of a line that passes through the points (-4,-1) and (5,7)?

1) y - 1 = 8/7(x + 4)
2) y - 1 = 8/9(x + 4)
3) y - 1 = 8/9(x - 4)
4) y = 98(x + 1)

Answer 1

The equation of a line in point-slope form that passes through the points (-4,-1) and (5,7) is y - 1 = 8/9(x + 4), which is option 2.

Step-by-step explanation:

The equation in point-slope form of a line that passes through the points (-4,-1) and (5,7) is found by first calculating the slope of the line using the formula Δy/Δx = (y2 - y1)/(x2 - x1). With the given points (-4, -1) and (5, 7), the slope is (7 - (-1))/(5 - (-4)) = 8/9. The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Using the point (-4,-1) and the calculated slope 8/9, the point-slope form is y - (-1) = 8/9(x - (-4)), which simplifies to y + 1 = 8/9(x + 4). So, the correct equation in point-slope form is y - 1 = 8/9(x + 4), which corresponds to option 2.