Methods of Algebraic Geometry

Algebraic geometry means to analyze the geometry by using the algebraic method.

The methods of algebraic geometry is

1. Cartesian coordinate system,

2. Slope of line,

3. Equation of line and

4. Distance between two points.

We will learn about the different methods of algebraic geometry example problems and practice problems are given below.
Example Problems: Methods of Algebraic Geometry:

Example problem 1:

Find the slope of line, which contains the two points A (13, 24), B (39, 48).

Solution:

By using the graphical method,

Slope

The slope of a line which contains two points (x1, y1) and (x2, y2) is given by,

Let us consider the following values, x1 = 13, x2 = 39, y1 = 24, y2 = 48

Slope of the line, m = ` (y_2 - y_1)/(x_2 - x_1)`

=  `(48 - 24)/(39 - 13)`

After simplify this, we get

= ` (24)/(26)`

Slope of the line (m) = 0.92

So, the slope of line, which contains the two points A (13, 24), B (39, 48) is 0.92

Example problem 2:

Find out the equation of line. Given slope is 4 and y intercept is 6

Solution:

Apply to the slope-intercept formula, the equation of the line is

Slope (m) = 4, y intercept(c) = 6

y = mx + c

y = 4x + 6

After simplify this, we get

4x - y + 6 = 0

The equation of line is 4x -y + 6 = 0

The above examples are helpful to helpful to study of methods of algebraic geometry.
Practice Problems: Methods of Algebraic Geometry:

Practice problem 1:

Find the slope of line, which contains the two points A (-20, 70), B (5, 2).

Slope of line = `-68/(25)`

Practice problem 2:

Find out the equation of line. Given slope is 5 and y intercept is 10

Equation of line: 5x - y + 10 = 0

Practice problem 3:

Find out the equation of line. Given slope is 12 and y intercept is 1

Equation of line: 12x - y + 1 = 0