Which point is the y-intercept of 2x − 5y = 10 on the graph?
Answer and explanation
Correct answer: (0, −2)
The governing concept is the coordinate definition of an intercept. A y-intercept is the point where a graph crosses the y-axis, and every point on the y-axis has x-coordinate 0. Substitute x = 0 in the equation: 2(0) − 5y = 10, so −5y = 10 and y = −2. Therefore the required point is (0, −2), which is option A. Option B has y = 0 and is an x-intercept candidate, while option C results from ignoring the negative sign. Option D does not satisfy the equation because 2(5) − 5(0) = 10, although it is actually the x-intercept.
Frequently asked questions
What is the correct answer to this question?
(0, −2)
Why is this the correct answer?
The governing concept is the coordinate definition of an intercept. A y-intercept is the point where a graph crosses the y-axis, and every point on the y-axis has x-coordinate 0. Substitute x = 0 in the equation: 2(0) − 5y = 10, so −5y = 10 and y = −2. Therefore the required point is (0, −2), which is option A. Option B has y = 0 and is an x-intercept candidate, while option C results from ignoring the negative sign. Option D does not satisfy the equation because 2(5) − 5(0) = 10, although it is actually the x-intercept.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
