Which equation represents the line that passes through the points (6, -3) and (-4, -9)?
(1 point)
y + 4 = 3/5 * (x + 9)
y + 4 = 5/3 * (x + 9)
y - 3 = 3/5 * (x + 6)
y + 3 = 3/5 * (x - 6)
To determine the equation of the line that passes through the points (6, -3) and (-4, -9), we can use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) represents one point on the line and m represents the slope of the line.
First, let's find the slope of the line using the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two given points:
m = (-9 - (-3)) / (-4 - 6)
m = (-9 + 3) / (-10)
m = -6 / -10
m = 3/5
Now that we have the slope, we can plug it into the point-slope form using one of the given points. Let's use the first point (6, -3):
y - (-3) = 3/5 * (x - 6)
y + 3 = 3/5 * (x - 6)
Therefore, the correct equation for the line that passes through the points (6, -3) and (-4, -9) is:
y + 3 = 3/5 * (x - 6)