What is the equation in point-slope form for a line that passes through the points (-6, 38) and
(2, -22)?
Responses
A
y + 38= – 15 (x – 6)
2y + 38= – 15 ( x – 6) 2
B
y – 38= – 2 (x + 6)
15y – 38= – 2 ( x + 6) 15
C
y + 38= – 2 (x – 6)
15y + 38= – 2 ( x – 6) 15
D
y – 38= – 15 (x + 6)
2
To find the equation in point-slope form for a line that passes through the points (-6, 38) and (2, -22), we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) represents one of the points and m represents the slope of the line.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (-22 - 38) / (2 - (-6))
m = -60 / 8
m = -15/2
Next, we choose one of the points, (-6, 38), and substitute the values into the point-slope form equation:
y - 38 = (-15/2)(x - (-6))
Simplifying, we have:
y - 38 = (-15/2)(x + 6)
Multiplying both sides by 2 to eliminate the fraction:
2(y - 38) = -15(x + 6)
Distributing:
2y - 76 = -15x - 90
Moving all terms to one side:
15x + 2y = -90 + 76
15x + 2y = -14
So the equation in point-slope form for the line passing through the points (-6, 38) and (2, -22) is:
15x + 2y = -14
Therefore, the correct answer is option D.