Question

Co-ordinates of the point at which the line \(2x - 7y = 14\) intersects the y-axis are :

• A. \((0, 2)\)
• B. \((0, -3)\)
• C. \((0, -2)\)
• D. \((0, 3)\)

Hint:

To find where a line intersects the y-axis (the y-intercept): 1. Set \(x = 0\) in the equation of the line. 2. Solve for \(y\). The point of intersection will be \((0, y)\). To find where a line intersects the x-axis (the x-intercept): 1. Set \(y = 0\) in the equation of the line. 2. Solve for \(x\). The point of intersection will be \((x, 0)\).

Answer 1

The Correct Option is C

Concept: A line intersects the y-axis at a point where the x-coordinate is zero. Step 1: Understanding the condition for y-axis intersection When a line intersects the y-axis, the value of its x-coordinate at that point is always 0. So, we need to find the y-coordinate when \(x=0\). Step 2: Substitute \(x=0\) into the given equation of the line The equation of the line is \(2x - 7y = 14\). Substitute \(x=0\) into this equation: \[ 2(0) - 7y = 14 \] \[ 0 - 7y = 14 \] \[ -7y = 14 \] Step 3: Solve for y Divide both sides by -7: \[ y = \frac{14}{-7} \] \[ y = -2 \] Step 4: Write the coordinates of the intersection point The x-coordinate is 0, and we found the y-coordinate to be -2. Therefore, the coordinates of the point where the line intersects the y-axis are \((0, -2)\). This matches option (3).