Find an equation for the line that contains the points (2, -3) and (6, 9).
find the first slope.
m = (y2 -y1)/(x2-x1)
m= (9-(-3))/(6-2)
m = 3
y-y1 = m(x-x1)
y - (-3) =3(x-2)
y + 3 = 3x -6
y + 3 -3 = 3x-6-3
y = 3x - 9
To find the equation for the line that contains two given points, you can use the slope-intercept form of a linear equation, which is:
y = mx + b
where:
- m is the slope of the line
- b is the y-intercept of the line
To find the slope (m) of the line passing through two points (x1, y1) and (x2, y2), you can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2, -3) and (6, 9), let's calculate the slope (m):
m = (9 - (-3)) / (6 - 2)
m = 12 / 4
m = 3
Now that we have the slope (m), we can substitute it into the slope-intercept form together with one of the given points (x1, y1) to find the value of b. Let's use the point (2, -3):
-3 = 3(2) + b
-3 = 6 + b
b = -9
Now we have both the slope (m = 3) and the y-intercept (b = -9). We can substitute these values back into the slope-intercept form to get the equation of the line:
y = 3x - 9
Therefore, the equation for the line that contains the points (2, -3) and (6, 9) is y = 3x - 9.