Question

Прямая проходит через точки A(0;-1 ) и В(2:5). Найти уравнение прямой.

Answer 1

Y = kx + b
A ( 0 ; - 1 )
B ( 2 ; 5 )
=====
- 1 = 0k + b
b = - 1
5 = 2k + b
2k = 5 - ( - 1 )
k = 6 : 2
k = 3
Ответ y = 3x - 1

Answer 2

Finding the Equation of a Line Passing Through Points A(0, -1) and B(2, 5)

To find the equation of the line passing through points A(0, -1) and B(2, 5), we can use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

Calculating the Slope (m)

The slope of the line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points through which the line passes.

Using the given points A(0, -1) and B(2, 5): m = (5 - (-1)) / (2 - 0) m = 6 / 2 m = 3

Substituting the Slope and a Point into the Point-Slope Form

Now that we have the slope, we can substitute it and one of the given points into the point-slope form to find the equation of the line.

Using point A(0, -1) and the slope m = 3: y - (-1) = 3(x - 0) y + 1 = 3x

So, the equation of the line passing through points A(0, -1) and B(2, 5) is y = 3x - 1.

This information is based on mathematical principles and calculations.