A third lineL3 passes through (-4,1) and is parallel to L2.find the equation
Since line L2 is parallel to line L3, they will have the same slope. To find the slope of line L2, we can use the given points (2,3) and (-7,1).
Using the slope formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points:
m = (1 - 3) / (-7 - 2)
m = -2 / -9
m = 2/9
Now that we have the slope of line L2, we can use the point-slope form to find the equation of line L3. The point-slope form is given by:
y - y1 = m(x - x1)
Substituting the given point (-4, 1) and the slope 2/9:
y - 1 = (2/9)(x - (-4))
y - 1 = (2/9)(x + 4)
y - 1 = (2/9)x + 8/9
y = (2/9)x + 17/9
Therefore, the equation of line L3 is y = (2/9)x + 17/9.