Question

Складіть рівняння прямої, яка проходить через точку А(3 под корнем; 5)

Answer 1

Уравнение прямой, проходящей через данную точку A(x1, y1) в данном направлении, определяемом угловым коэффициентом k,

y - y1 = k(x - x1).

у+5=к(х-sqrt{3})

у=к(х-sqrt{3})-5

Answer 2

Equation of a Line Passing Through Point A(3+sqrt(5), 5)

To find the equation of a line passing through point A(3+sqrt(5), 5), we need to determine the slope of the line and the y-intercept.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

Since we have a specific point on the line, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Let's find the slope first.

The change in x is the difference between the x-coordinate of the given point and another x-coordinate on the line. Similarly, the change in y is the difference between the y-coordinate of the given point and another y-coordinate on the line.

Since we don't have another point on the line, we can't directly calculate the slope. However, we can use the fact that the slope of a line passing through two points is the same as the slope of a line passing through any two points on that line.

Let's consider another point B(x, y) on the line. The slope between points A and B will be the same as the slope between points A and B.

Now, let's choose another point B on the line. For simplicity, let's choose B(0, b), where b is a constant.

Using the slope formula, we have:

slope = (change in y) / (change in x) = (5 - b) / (3 + sqrt(5) - 0) = (5 - b) / (3 + sqrt(5))

Now, we can use the point-slope form of a linear equation to write the equation of the line passing through point A(3+sqrt(5), 5):

y - 5 = [(5 - b) / (3 + sqrt(5))](x - (3 + sqrt(5)))

Simplifying the equation, we get:

y - 5 = [(5 - b) / (3 + sqrt(5))](x - 3 - sqrt(5))

This is the equation of the line passing through point A(3+sqrt(5), 5).

Please note that the value of b can be any real number, as long as it satisfies the equation.

Let me know if there's anything else I can help you with!