Question

Y=kx+b График симметричен относительно начало кординат ,проходит А(2,10). Найти чему равна сумма k и b? Помогите

Answer 1

Графику принадлежат две точки (0 ; 0 ) и (2; 10). Подставим их координаты в уравнение:
0 = b
10 = 2k +b      это система

b = 0
k = 5

k + b = 5

Answer 2

Finding the Sum of k and b in the Equation y = kx + b

To find the sum of k and b in the equation y = kx + b, we can use the given information that the graph is symmetric with respect to the origin and passes through the point A(2,10).

Let's break down the problem step by step:

1. Symmetry with respect to the origin: - When a graph is symmetric with respect to the origin, it means that if a point (x, y) lies on the graph, then the point (-x, -y) also lies on the graph. - In this case, since the graph passes through point A(2,10), we can conclude that the point (-2,-10) also lies on the graph.

2. Using the points to find the equation: - We have two points on the graph: A(2,10) and (-2,-10). - We can use these points to form two equations and solve for k and b. - Let's use the point-slope form of a linear equation: y - y1 = m(x - x1). - For point A(2,10), the equation becomes: y - 10 = k(x - 2). - For point (-2,-10), the equation becomes: y - (-10) = k(x - (-2)).

3. Simplifying the equations: - The first equation simplifies to: y - 10 = kx - 2k. - The second equation simplifies to: y + 10 = kx + 2k.

4. Finding the sum of k and b: - To find the sum of k and b, we need to isolate k in both equations. - In the first equation, we can rewrite it as: y = kx - 2k + 10. - In the second equation, we can rewrite it as: y = kx + 2k - 10. - By comparing the equations, we can see that b = -2k + 10 and b = 2k - 10. - Equating these two expressions for b, we get: -2k + 10 = 2k - 10. - Solving this equation, we find: 4k = 20, which gives us k = 5. - Substituting k = 5 into either expression for b, we find: b = -2(5) + 10 = 0.

5. Sum of k and b: - The sum of k and b is k + b = 5 + 0 = 5.

Therefore, the sum of k and b in the equation y = kx + b is 5.