Graph coordinates calculator how to#

In fact, the calculation is quite generic, so it can also calculate the area of parallelogram, square, rhombus, trapezoid, kite, etc., that is, the area of any convex quadrilateral. Note that in the case of a horizontal line, the vertical displacement is zero because the line runs parallel to the x-axis. The online calculator below calculates the area of a rectangle, given coordinates of its vertices. Note that in the case of a vertical line, the horizontal displacement is zero because the line runs parallel to the y-axis. Note that if, then and if, then Equation of a vertical line Once we have direction vector from to, our parametric equations will be This vector quantifies the distance and direction of an imaginary motion along a straight line from the first point to the second point. We need to find components of the direction vector also known as displacement vector. Let's find out parametric form of a line equation from the two known points and. Write the final line equation (we omit the slope, because it equals one):Īnd here is how you should enter this problem into the calculator above: slope-intercept line equation example Parametric line equations.

Calculate the intercept b using coordinates of either point.Problem: Find the equation of a line in the slope-intercept form given points (-1, 1) and (2, 4)

Graph coordinates calculator how to#

The line equation, in this case, becomes How to find the slope-intercept equation of a line example Note that in the case of a horizontal line, the slope is zero and the intercept is equal to the y-coordinate of points because the line runs parallel to the x-axis. The line equation, in this case, becomes Equation of a horizontal line Note that in the case of a vertical line, the slope and the intercept are undefined because the line runs parallel to the y-axis. So, once we have a, it is easy to calculate b simply by plugging or to the expression above.įinally, we use the calculated a and b to write the result as įor two known points we have two equations in respect to a and b Let's find slope-intercept form of a line equation from the two known points and. For non-linear functions, the rate of change of a curve varies, and the derivative of a function at a given point is the rate of change of the function, represented by the slope of the line tangent to the curve at that point.How to find the equation of a line in slope-intercept form While this is beyond the scope of this calculator, aside from its basic linear use, the concept of a slope is important in differential calculus. Given the points (3,4) and (6,8) find the slope of the line, the distance between the two points, and the angle of incline: m = Given two points, it is possible to find θ using the following equation: The above equation is the Pythagorean theorem at its root, where the hypotenuse d has already been solved for, and the other two sides of the triangle are determined by subtracting the two x and y values given by two points.

Refer to the Triangle Calculator for more detail on the Pythagorean theorem as well as how to calculate the angle of incline θ provided in the calculator above. Since Δx and Δy form a right triangle, it is possible to calculate d using the Pythagorean theorem. Use rectangular, polar, cylindrical, or spherical coordinates. It can also be seen that Δx and Δy are line segments that form a right triangle with hypotenuse d, with d being the distance between the points (x 1, y 1) and (x 2, y 2). Graph inequalities, contour plots, density plots and vector fields. In the equation above, y 2 - y 1 = Δy, or vertical change, while x 2 - x 1 = Δx, or horizontal change, as shown in the graph provided. The slope is represented mathematically as: m = In the case of a road, the 'rise' is the change in altitude, while the 'run' is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. Slope is essentially the change in height over the change in horizontal distance, and is often referred to as 'rise over run.' It has applications in gradients in geography as well as civil engineering, such as the building of roads.

A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator.

A line has a constant slope, and is horizontal when m = 0.

A line is decreasing, and goes downwards from left to right when m < 0.

A line is increasing, and goes upwards from left to right when m > 0.

Given m, it is possible to determine the direction of the line that m describes based on its sign and value: The larger the value is, the steeper the line. Generally, a line's steepness is measured by the absolute value of its slope, m. Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m.