A third lineL3 passes through (-4,1) and is parallel to L2.find the equation

Answer 1

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.