What is the equation for a line that passes through the points (2,1) and (-4,4)
A: y=-1/2x+2
b: y=1/2x+2
c: y=-1/2x-2
d: y=1/2x-2
(2,1), (-4,4).
m = (4-1) / (-4-2) = 3/-6 = -1/2.
Y = mx + b,
Y = (-1/2)2 + b = 1,
b = 2.
Eq: Y = -(1/2)X + 2.
Answer = A.
To find the equation of the line that passes through the points (2,1) and (-4,4), you can use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of a point on the line, and m is the slope of the line.
First, calculate the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁), where (x₂, y₂) are the coordinates of the second point (-4,4), and (x₁, y₁) are the coordinates of the first point (2,1).
m = (4 - 1) / (-4 - 2) = 3 / -6 = -1/2
So, we have the slope of the line, which is -1/2.
Next, choose one of the given equations and substitute the coordinates of one of the points (x₁, y₁) into the equation.
Let's check option A: y = -1/2x + 2.
Using the point (2,1) in place of x and y:
1 = -1/2(2) + 2
1 = -1 + 2
1 = 1 (True)
Since the equation fits the point (2,1), it is a valid equation.
Now, let's also check another point, (-4,4), to be more certain.
Using option A: y = -1/2x + 2
Using the point (-4,4) in place of x and y:
4 = -1/2(-4) + 2
4 = 2 + 2
4 = 4 (True)
Since the equation also fits the point (-4,4), we can conclude that Option A: y = -1/2x + 2 is the correct equation for the line passing through the points (2,1) and (-4,4).