find the equation of the line L that passes through the point (-2,4) and satisfies the given condition.
L passes thrugh the point (3,7/2)
To find the equation of the line L that passes through the point (-2,4) and also passes through the point (3,7/2), we can use the point-slope form of the equation of a line.
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) are the coordinates of a point on the line.
First, let's find the slope (m) using the given points (-2,4) and (3,7/2).
m = (y₂ - y₁) / (x₂ - x₁)
m = (7/2 - 4) / (3 - (-2))
m = (7/2 - 8/2) / (3 + 2)
m = (-1/2) / 5
m = -1/10
Now that we have the slope (m), we can substitute it along with the coordinates of one of the given points into the point-slope form of the equation of a line. Let's use the point (-2,4):
y - 4 = (-1/10)(x - (-2))
Simplifying:
y - 4 = (-1/10)(x + 2)
Distribute the (-1/10):
y - 4 = (-1/10)x - (1/10)(2)
y - 4 = (-1/10)x - 2/10
Combine like terms:
y - 4 = (-1/10)x - 1/5
Add 4 to both sides to isolate y:
y = (-1/10)x - 1/5 + 4
Simplify the fraction:
y = (-1/10)x - 1/5 + 20/5
y = (-1/10)x + 19/5
Therefore, the equation of the line L that passes through the point (-2,4) and also passes through the point (3,7/2) is y = (-1/10)x + 19/5.