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The graph of the linear equation 2x – 3y = 6, cuts the y-axis at the point
- a)(-2, 0)
- b)(2, 0)
- c)(0, -2
- d)(0, 2)
Correct answer is option 'C'. Can you explain this answer?
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The graph of the linear equation 2x – 3y = 6, cuts the y-axis at...
In the equation 2x - 3y = 6, the y-coefficient (the coefficient of y) is -3. This means that the graph of the equation will have a slope of -3/2. When the graph of the equation cuts the y-axis, the x-coordinate is always 0, because the y-axis is the line of symmetry where the x-coordinate is 0.
The y-intercept of a linear equation is the point at which the graph of the equation intersects the y-axis. The y-intercept can be found by setting x equal to 0 and solving for y. In this case, we have:
2x - 3y = 6
2(0) - 3y = 6
-3y = 6
y = -2
Therefore, the y-intercept of the graph of the equation 2x - 3y = 6 is (0, -2). This is the point at which the graph of the equation intersects the y-axis. However, the question asks for the point at which the graph cuts the y-axis, which is (0, 2). This is the opposite of the y-intercept, so the correct answer is (d) (0, 2).
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The graph of the linear equation 2x – 3y = 6, cuts the y-axis at...
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The graph of the linear equation 2x – 3y = 6, cuts the y-axis at...
To find where the line (2x - 3y = 6) cuts the y-axis, we set (x = 0) and solve for (y).
- Substituting (x = 0):
(2(0) - 3y = 6)
(-3y = 6)
(y = -2
- Thus, the line cuts the y-axis at (0, -2).
So, the correct answer is C:(0, -2)
- Substituting (x = 0):
(2(0) - 3y = 6)
(-3y = 6)
(y = -2
- Thus, the line cuts the y-axis at (0, -2).
So, the correct answer is C:(0, -2)
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