The equation of the line in the general form is x + y - 2 = 0 ⇒ 2nd answer
Step-by-step explanation:
The general form of the equation of a line is Ax + By + C = 0,where
∵ The line passes through point (1 , 1)
- Substitute x and y in the form of the equations by the coordinates
of the point
∵ Ax + By + C = 0
∵ x = 1 and y = 1
∴ A(1) + B(1) + C = 0
∴ A + B + C = 0 ⇒ (1)
∵ The y-intercept is 2
- That means the line intersects the y-axis at point (0 , 2)
∴ The line passes through point (0 , 2)
∵ x = 0 and y = 2
∴ A(0) + B(2) + C = 0
∴ 2B + C = 0
- Subtract 2B from both sides
∴ C = -2B ⇒ (2)
Substitute (2) in (1)
∴ A + B + (-2B) = 0
∴ A + B - 2B = 0
∴ A - B = 0
- Add B to both sides
∴ A = B
In the equation the coefficients of x and y are equal and C is twice
negative the coefficient of y
Let us look for the equation which has these conditions above
In the equation x + y - 2 = 0
∵ A = 1
∵ B = 1
∵ C = -2
∴ A = B and C = -2B
∴ The equation of the line is x + y - 2 = 0
The equation of the line in the general form is x + y - 2 = 0
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You can learn more about the equation of a line in brainly.com/question/12941985
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