Question

1)Составьте уравнение прямой, проходящей через точки А(2;-3) и В(4;1).2)Найдите координаты точки пересечения данной прямой с осью абсцисс.

Answer 1

1. уравнение прямой: y=kx+b

подставим координаты в уравнение: -3=2k+b и 1=4k+b

из второго уравнения: b=1-4k

теперь подставим b в первое уравнение: -3=2k+1-4k => -3-1=2k-4k => -4=-2k =>k=2

 

теперь подставим k во второе уравнение: 1=4*2+b
                                                                                 b=1-8

                                                                                 b=-7

следовательно уравнение принимает вид: y=2x-7

 

2. теперь подставим y=0 . получается 0=2*х-7 

                                                                       2х=7

                                                                       х=3,5                значит (3,5; 0)  

Answer 2

I will answer your question in detail. 1) To find the equation of the line passing through the points A(2;-3) and B(4;1), we need to use the formula:

y - y1 = k * (x - x1)

where k is the slope of the line and (x1, y1) is any point on the line. We can use the coordinates of A or B as (x1, y1). To find k, we can use the formula:

k = (y2 - y1) / (x2 - x1)

where (x2, y2) is the other point on the line. Using the coordinates of A and B, we get:

k = (1 - (-3)) / (4 - 2) = 4 / 2 = 2

Now we can substitute k and the coordinates of A into the first formula:

y - (-3) = 2 * (x - 2)

Simplifying, we get:

y + 3 = 2x - 4

y = 2x - 7

This is the equation of the line passing through A and B. You can also check the answer using the [online calculator](https://ru.onlinemschool.com/math/assistance/cartesian_coordinate/p_to_line/).

2) To find the coordinates of the point where the line intersects the x-axis, we need to set y equal to zero and solve for x:

y = 2x - 7

0 = 2x - 7

2x = 7

x = 7 / 2

The x-coordinate of the point is 7 / 2. The y-coordinate is zero by definition. Therefore, the point of intersection is (7 / 2, 0). You can also see the graph of the line and the point using the [online calculator](https://ru.onlinemschool.com/math/assistance/cartesian_coordinate/p_to_line/).