Which equation represents the line that passes through the points (6, –3) and (–4, –9)?
(1 point)
Responses
equation
Image with alt text: equation
equation
Image with alt text: equation
equation
Image with alt text: equation
equation
The equation of a line passing through two points (x1, y1) and (x2, y2) is found using the slope-intercept form:
y - y1 = m(x - x1)
Where m is the slope of the line.
Given the points (6, -3) and (-4, -9), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-9 - (-3)) / (-4 - 6)
m = (-9 + 3) / (-4 - 6)
m = -6 / -10
m = 3/5
Now that we have the slope, we can use the point-slope form with one of the points:
y - (-3) = (3/5)(x - 6)
Simplified:
y + 3 = (3/5)(x - 6) [equation 1]
Multiplying through by 5 to eliminate the fraction:
5(y + 3) = 3(x - 6)
5y + 15 = 3x - 18
Rearranging:
3x - 5y = 33 [equation 2]
So, the equation of the line passing through the points (6, -3) and (-4, -9) is either equation 1 or equation 2.