By substitution
There are a couple ways to determine the equation of a line without graphing. How to proceed depends on what you know about the line. Do you know a point, (x1, y1), and slope, m? Then use the point-slope formula, Do you know two points on the line, say (x1, y1) and (x2, y2)? Then use the two-point formula,
An equation that relates x and y coordinates defines a specific relationship between the two variables, allowing you to determine the position of points on the xy-plane. For example, a linear equation like (y = mx + b) gives you the y-coordinate for any given x-coordinate, and vice versa. By substituting different values of x or y into the equation, you can generate a set of points that lie on the graph of the equation, illustrating the relationship visually on the plane. This ability to derive coordinates from an equation is fundamental in analyzing and graphing mathematical relationships.
Subtract the equation of one line from the equation of the other
If you have an equation that looks like y=mx+b then the m is the slope. If you have two points then you use the formula Y2-Y1/X2-X1
The x and y coordinates
You must find the slope, if it is positive, then the line is always increasing. If it is negative, then the line is always decreasing.
guess it
There are a couple ways to determine the equation of a line without graphing. How to proceed depends on what you know about the line. Do you know a point, (x1, y1), and slope, m? Then use the point-slope formula, Do you know two points on the line, say (x1, y1) and (x2, y2)? Then use the two-point formula,
Graph the equation then find the x intercepts.
An equation that relates x and y coordinates defines a specific relationship between the two variables, allowing you to determine the position of points on the xy-plane. For example, a linear equation like (y = mx + b) gives you the y-coordinate for any given x-coordinate, and vice versa. By substituting different values of x or y into the equation, you can generate a set of points that lie on the graph of the equation, illustrating the relationship visually on the plane. This ability to derive coordinates from an equation is fundamental in analyzing and graphing mathematical relationships.
Subtract the equation of one line from the equation of the other
Assume the equation is y = kx + c Put in the x and y values of your known coordinates and sove the simultaneous equations.
If you have an equation that looks like y=mx+b then the m is the slope. If you have two points then you use the formula Y2-Y1/X2-X1
Yes if it is a straight line equation
The x and y coordinates
To find the length of a side, you either measure it, or you calculate it. How you calculate it depends on what data is given. For example, if you have the coordinates of the endpoints of a line, you can calculate the length by using the Pythagorean theorem (or simply subtracting the coordinates of the two endpoints, if the line is perfectly vertical or perfectly horizontal).
Yes if it is a straight line equation