Table of Contents
What is general equation of first degree?
A first-degree equation with two variables whose exponents are 0 or 1 that is expressed in the general form Ax + By + C = 0, where the coefficients A and B are not zero. A first-degree equation in two variables generally has an infinite number of solutions.
Under what condition is the general equation ax by c 0 of the first degree X and Y represents a line?
When we say that a first degree equation in x, y i.e., ax + by + c = 0 represents a line, it means that all points (x, y) satisfying ax + by + c = 0 lies along a line. Thus a line is also defined as the locus of a point satisfying the condition ax + by + c = 0 where a, b, c are constants.
How do you prove the equation of a straight line?
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
How do you find first and first degree?
A differential equation of first order and first degree can be written as f( x, y, dy/dx) = 0. A differential equation of first order and first degree can be written as f( x, y, dy/dx) = 0.
What are the conditions for a straight line?
A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.
What is the condition for a B and C lying on a straight line?
Collinear points: Three points A, B and C are said to be collinear if they lie on the same straight line. There points A, B and C will be collinear if AB + BC = AC as is clear from the adjoining figure.
How do you determine the equation of a line?
How to Find the Equation of a Line from Two Points
- Find the slope using the slope formula.
- Use the slope and one of the points to solve for the y-intercept (b).
- Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
What is the general form of equation?
The general form of any equation contains the degree of variables in decreasing order. The general form of a linear equation is ax + b = 0. The general form of a linear equation in two variables is ax + by + c = 0. We know that the general form of the equation of lines can be found using the slope and y-intercept.
How do you find the general equation of a straight line?
Thus, every point on the line segment joins P and Q lines on ax + by + c = 0. Hence, ax + by + c = 0 corresponds to a straight line. The general equation of a straight line y = m * x + c.
How to prove a line is a straight line?
We define a straight line as a curve where every point on the line segment joining any two points lies on it. Let’s throw light on the coordinate geometry to prove that every first-degree equation in x, y represents a straight line. Let ax + by + c = 0 be a first-degree equation in x,y where a, b, and c are constant.
Is the equation of a plane a first-degree equation?
We can show that if we assume the equation of a plane as a first-degree equation in x, y and z, the above property is satisfied. Assume a curve a x + b y + c z + d = 0. Let points P 1 ( x 1, y 1, z 1) and P 2 ( x 2, y 2, z 2) lie on the curve, so we get the following equations:
What is the general equation of a line in two variables?
The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers. When we represent the equation geometrically, we always get a straight line.