Which equation represents the line that passes through the points (6, -3) and (-4, -9)?
The equation of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the slope-intercept form: y - y₁ = m(x - x₁), where m is the slope of the line.
First, let's find the slope (m) of the line passing through the points (6, -3) and (-4, -9).
m = (y₂ - y₁) / (x₂ - x₁)
m = (-9 - (-3)) / (-4 - 6)
m = (-9 + 3) / (-4 - 6)
m = -6 / -10
m = 3/5
Now, let's substitute the slope (m) and one of the points (x₁, y₁) into the slope-intercept form:
y - y₁ = m(x - x₁)
y - (-3) = (3/5)(x - 6)
y + 3 = (3/5)(x - 6)
Multiplying both sides by 5 to eliminate the fraction:
5(y + 3) = 3(x - 6)
5y + 15 = 3x - 18
To have the equation in the form y = mx + b, we need to isolate y:
5y = 3x - 18 - 15
5y = 3x - 33
y = (3/5)x - (33/5)
Therefore, the equation of the line passing through the points (6, -3) and (-4, -9) is y = (3/5)x - (33/5).