Final answer:
The equation of the line in point-slope form that passes through the points (2, -3) and (-1, 9) is found by calculating the slope, which is -4, and using one of the points to write the equation. The correct equation is y = -4x + 5.
Step-by-step explanation:
To find the equation of the line in point-slope form that passes through the points (2, -3) and (-1, 9), we first need to calculate the slope of the line. The slope (m) is given by the change in y over the change in x, so:
m = (y2 − y1) / (x2 − x1)
m = (9 − (-3)) / (-1 − 2)
m = (9 + 3) / (-1 - 2)
m = 12 / (-3)
m = -4
Now we have the slope and one point, we can plug it into the point-slope formula, y − y1 = m(x − x1), which gives us:
y − (-3) = -4(x − 2)
y + 3 = -4x + 8
y = -4x + 5
Answer: A) y = -4x + 5