Home
Class 10
MATHS
The line x - y = 8 intersect y - axis at...

The line `x - y = 8` intersect y - axis at `(0,-8)`. [True/False]

Text Solution

AI Generated Solution

The correct Answer is:
To determine whether the statement "The line x - y = 8 intersects the y-axis at (0, -8)" is true or false, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Equation of the Line**: The given equation of the line is \( x - y = 8 \). 2. **Identify the Point of Intersection with the Y-Axis**: To find where the line intersects the y-axis, we set \( x = 0 \) because any point on the y-axis has an x-coordinate of 0. 3. **Substitute x = 0 into the Equation**: Substitute \( x = 0 \) into the equation: \[ 0 - y = 8 \] 4. **Simplify the Equation**: This simplifies to: \[ -y = 8 \] 5. **Solve for y**: To find y, multiply both sides by -1: \[ y = -8 \] 6. **Determine the Point of Intersection**: Thus, the coordinates of the intersection point with the y-axis are \( (0, -8) \). 7. **Check the Statement**: The statement claims that the line intersects the y-axis at \( (0, -8) \). Since we found the intersection point to be \( (0, -8) \), the statement is indeed true. ### Conclusion: The statement "The line x - y = 8 intersects the y-axis at (0, -8)" is **True**. ---
Promotional Banner

Topper's Solved these Questions

  • PRACTICE TEST-II

    CBSE COMPLEMENTARY MATERIAL|Exercise Section B|6 Videos

  • PRACTICE TEST-II

    CBSE COMPLEMENTARY MATERIAL|Exercise Section C|14 Videos

  • PRACTICE TEST-1

    CBSE COMPLEMENTARY MATERIAL|Exercise SECTION-C|14 Videos

  • PROBABILITY

    CBSE COMPLEMENTARY MATERIAL|Exercise PRACTICE-TEST|11 Videos

Similar Questions

Explore conceptually related problems

The co-ordinate where the line x-y = 8 will intersect y-axis is ……..

Let the line 2x+3y=18 intersect the y-axis at B .Suppose C(!=B), with coordinates (a,b), is a point on the line such that PB=PC, where P=(10,10). Then 8a+2b equals

The condition for the line 4x+3y+k=0 to intersect y^2= 8x is kgtm ,then m is equal to

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at Aa n dB , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a)3x-4y+2=0 (b)4x+3y+7=0 (c)6x-8y+7=0 (d) none of these

Find the co-ordinate where the line x-y =8 will intersect y-axis .

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . The locus of R and the circle x^2 + y^2 - 8y - 4 = 0 (A) touch each other internally (B) touche the given circle externally (C) intersect in two distinct points (D) neither intersect nor touch each other

If the line x-y-1=0 intersect the parabola y^(2)=8x at P and Q, then find the point on intersection of tangents P and Q.

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Image of the locus of R in the line y = - x is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0