Find an equation of the line that contains the following pair of points. (-2,-3) and (-6,-9)
slope = (-9+3)/(-6+2) = -6/-4 = 3/2
y+3 = (3/2)(x+2)
2y + 6 = 3x + 6
3x - 2y = 0
To find the equation of a line that passes through two points, you can use the slope-intercept form of a linear equation:
y = mx + b
where:
- y and x are the coordinates of any point on the line
- m represents the slope of the line
- b is the y-intercept (the value of y when x = 0)
To find the slope (m) of the line passing through the points (-2,-3) and (-6,-9), you can use the slope formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let's calculate the slope:
m = (-9 - (-3))/(-6 - (-2))
= (-9 + 3)/(-6 + 2)
= -6/-4
= 3/2
Now that we have the slope (m), we can use any of the two given points and substitute the values into the slope-intercept form to find the y-intercept (b). Let's choose the point (-2,-3):
-3 = (3/2)(-2) + b
-3 = -3 + b
b = -3 - (-3)
b = -3 + 3
b = 0
Now we have the slope (m = 3/2) and y-intercept (b = 0). We can plug these values into the slope-intercept form to get the equation of the line:
y = (3/2)x + 0
Simplifying it, we get:
y = (3/2)x
Therefore, the equation of the line passing through the points (-2,-3) and (-6,-9) is y = (3/2)x.