Which equation represents the line that passes through the points (6, –3) and (–4, –9)?
(1 point)
Responses
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 find the equation of a line passing through two points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) represents one of the points and m represents the slope of the line.
First, we need to find the slope:
m = (y2 - y1) / (x2 - x1)
Using the points (6, -3) and (-4, -9):
m = (-9 - (-3)) / (-4 - 6)
m = (-9 + 3) / (-4 - 6)
m = -6 / -10
m = 3/5
Now, we can choose one of the given points to substitute into the point-slope form. Let's use (6, -3):
y - (-3) = (3/5)(x - 6)
y + 3 = (3/5)(x - 6)
y + 3 = (3/5)x - (3/5)(6)
y + 3 = (3/5)x - 18/5
To have the equation in standard form, we can rearrange it:
y = (3/5)x - 18/5 - 3
y = (3/5)x - 18/5 - 15/5
y = (3/5)x - 33/5
Therefore, the correct equation that represents the line passing through the points (6, -3) and (-4, -9) is y = (3/5)x - 33/5. However, this equation is not one of the given options. None of the given options accurately represent the equation of the line passing through the given points.