Maths-
General
Easy
Question
Identify the line having y-intercept = 1/2
- y = 2x + 1
- x = 2y +2
- 4y – 8x = 2
- x = 2y
Hint:
Y-intercept for a line is a point at which the given line intersects with the y-axis i.e. the point at which x = 0.
The correct answer is: 4y – 8x = 2
Step-by-step solution:-
The given line has y-intercept = 1/2.
y-intercept is the point at which x-coordinate is 0
∴ The given point is (0,1/2)
We substitute (0,1/2) in the given equations to find whether LHS = RHS or not.
a. y = 2x + 1
∴ 1/2 = 2 (0) + 1
∴ 1/2 = 0 + 1
∴ 1/2 ≠ 1
∴ LHS ≠ RHS
b. x = 2y +2
∴ 0 = 2 (1/2) + 2
∴ 0 = 1 + 2
∴ 0 ≠ 3
∴ LHS ≠ RHS
c. 4y – 8x = 2
∴ 4 (1/2) - 8 (0) = 2
∴ 2 - 0 = 2
∴ 2 = 2
∴ LHS = RHS
d. x = 2y
∴ 0 = 2 (1/2)
∴ 0 ≠ 1
∴ LHS ≠ RHS
Final Answer:-
∴ Option c i.e. 4y - 8x = 2 is the correct option.
Note:-
Alternatively, we can simplify the given equations and compare it with slope-intercept formula to find the value of y-intercepts-
a. y = 2x + 1
∴ Comparing this equation with y = mx + b, we get b = 1 ≠ 1/2
b. x = 2y +2
∴ x - 2 = 2y
∴ (x - 2) / 2 = y
∴ 1/2 x - 2/2 = y
∴ 1/2 x - 1 = y
i.e. y = 1/2 x - 1
Comparing this equation with y = mx + b, we get b = -1 ≠ 1/2
c. 4y – 8x = 2
∴ 2y - 4x = 1 .................. (Dividing both sides by 2)
∴ 2y = 4x + 1
∴ y = 2x + 1/2 ...... (Dividing both sides by 2)
∴ Comparing this equation with y = mx + b, we get b = 1/2
d. x = 2y
∴ 1/2 x = y ................. (Dividing both sides by 2)
i.e. y = 1/2 x + 0
Comparing this equation with y = mx + b, we get b = 0 ≠ 1/2
∴ Option c i.e. 4y - 8x = 2 has y-intercept = 1/2
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Find the value of p so that
![left parenthesis 4 divided by 5 right parenthesis cubed divided by left parenthesis 4 divided by 5 right parenthesis to the power of negative 3 end exponent equals left parenthesis 4 divided by 5 right parenthesis to the power of 3 p end exponent](data:image/png;base64,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)
Maths-General