Find an equation of the line L that passes though the point (-2,4) and satisfies the condition.
L passes through the point (3, 7/2)
P1(x1,y1)=(-2,4)
P2(x2,y2)=(3, 7/2)
line passing through P1 and P2:
L : (y-y1)/(y2-y1) = (x-x1)/(x2-x1)
Substitute and simplify.
To find the equation of a line that passes through a given point and satisfies a condition, we will use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope of the line.
Let's start by finding the slope of the line using the given points (-2, 4) and (3, 7/2). The slope (m) is given by:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates, we have:
m = (7/2 - 4) / (3 - (-2))
m = (-1/2) / (3 + 2)
m = (-1/2) / 5
m = -1/10
Now that we have the slope, we can choose either of the given points to substitute into the point-slope form. Let's use the point (-2, 4):
y - 4 = (-1/10)(x - (-2))
y - 4 = (-1/10)(x + 2)
y - 4 = (-1/10)x - 1/5
To put the equation in standard form, we can multiply both sides by 10 to eliminate fractions:
10(y - 4) = -x - 2
10y - 40 = -x - 2
x + 10y = 38
Therefore, the equation of the line L that passes through the point (-2, 4) and satisfies the condition is x + 10y = 38.