Question

Каким будет уравнение прямой проходящей через точки с координатами (4;3) и (6;15)?

Answer 1

Решение смотри на фото

Answer 2

Equation of a Line Passing Through Two Points

To find the equation of a line passing through two points, we can use the point-slope form of a linear equation, which is given by:

y - y1 = m(x - x1)

Where: - (x1, y1) and (x, y) are the coordinates of the given points. - m is the slope of the line.

Calculating the Slope

First, we need to calculate the slope (m) using the given points (4, 3) and (6, 15).

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1)

Substituting the given points: m = (15 - 3) / (6 - 4) m = 12 / 2 m = 6

Using the Point-Slope Form

Now that we have the slope, we can use the point-slope form to find the equation of the line passing through the given points.

Using the point (4, 3): y - 3 = 6(x - 4)

This is the equation of the line passing through the points (4, 3) and (6, 15).

Final Equation

Expanding the equation: y - 3 = 6x - 24

Solving for y: y = 6x - 21

So, the equation of the line passing through the points (4, 3) and (6, 15) is: y = 6x - 21