Question

Даны функции y = 6x + 9 и y = 3x + 4,5 Без построения графиков функций, узнай координаты точки, в которой они пересекутся.

Answer 1

Ответ:

$(-1,5; 0)$

Объяснение:

$y=6x+9, \quad y=3x+4,5 \Rightarrow 6x+9=3x+4,5;$

$6x-3x=4,5-9;$

$3x=-4,5;$

$x=-1,5;$

$y(-1,5)=6 \cdot (-1,5)+9=-9+9=0;$

$(-1,5; 0);$

Answer 2

Finding the Intersection Point of Two Functions Without Graphing

To find the coordinates of the point where the two functions intersect, we can set the two functions equal to each other and solve for the value of x. Once we have the value of x, we can substitute it into either of the original functions to find the corresponding y-coordinate.

The given functions are: - y = 6x + 9 - y = 3x + 4.5

Solving for the Intersection Point

Setting the two functions equal to each other: 6x + 9 = 3x + 4.5

Subtracting 3x from both sides: 3x + 9 = 4.5

Subtracting 4.5 from both sides: 3x = -4.5

Dividing by 3: x = -1.5

Finding the y-coordinate

Substituting x = -1.5 into either of the original functions: For y = 6x + 9: y = 6(-1.5) + 9 y = -9 + 9 y = 0

So, the coordinates of the point where the two functions intersect are (-1.5, 0).