Bring the general equation of the straight line 3x-4y + 12 = 0 to the equation in segments and calculate

| July 28, 2021 | education

Bring the general equation of the straight line 3x-4y + 12 = 0 to the equation in segments and calculate the length of the segment that is cut off from this straight line by the corresponding coordinate angle.

As you know, the equation of a straight line in segments on a plane in a rectangular coordinate system Oxy has the form x / a + y / b = 1, where a and b are some nonzero real numbers.
In order to bring this general equation of the straight line 3 * x – 4 * y + 12 = 0 to an equation in segments, move the number 12 from the left side of the equation to the right side. We have: 3 * x – 4 * y = –12. Divide both sides of the resulting equation by (–12). Then, we get: x / (–4) + y / 3 = 1. The resulting equation is an equation in the segments of this straight line with the values: a = –4 and b = 3.
The resulting equation allows us to assert that this straight line passes through points (in other words, intersects the coordinate axes) with coordinates: A (–4; 0) and B (0; 3).
Now let’s calculate the length of the segment that is cut off from this straight line by the corresponding coordinate angle, that is, we will find the length of the segment AB. To do this, use the formula for calculating the distance between two points A (xa; ya) and B (xb; yb) on the plane: AB = √ ((xb – xa) ² + (yb – ya) ²). We have: AB = √ ((0 – (–4)) ² + (3 – 0) ²) = √ (16 + 9) = √ (25) = 5.
Answer: x / (–4) + y / 3 = 1 and 5.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.