![]() ![]() 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. 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: where a is the slope of the line, and b is the y-intercept, and your objective to find both. 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. This slope-intercept equation calculator will allow you to provide information of a linear equation in one of four ways, and then it will show how to put it into slope-intercept form, with the following formula: y ax + b y ax+b. 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. 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). 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 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. Using the equation y = 3x - 6, set x=0 to find the y-intercept.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. x & y intercepts of Slope Intercept Form. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. It is the point where the line crosses the y axis. Explore math with our beautiful, free online graphing calculator. The y-intercept of a line is the value of y when x=0. Slope is the coefficient of x so in this case slope = 3 This is slope intercept form, y = 3x - 6.You want to get y by itself on one side of the equation, so you need to divide both sides by 2 to get y = 3x - 6.Subtract 12 from both sides of the equation to get 6x - 12 = 2y.Add 2y to both sides to get 6x = 12 + 2y.Your goal is to get the equation into slope intercept format y = mx + b You have the equation of a line, 6x - 2y = 12, and you need to find the slope. If you have the equation for a line you can put it into slope intercept form. Slope intercept form y = 2x + 1 becomes 2x - y = -1 written in standard form. ![]() Subtract 1 from both sides of the equation to get 2x - y = -1 Subtract y from both sides of the equation to get 2x - y + 1 = 0 Note that the equation should not include fractions or decimals, and the x coefficient should only be positive. Use either the point slope form or slope intercept form equation and work out the math to rearrange the equation into standard form. You may also see standard form written as Ax + By + C = 0 in some references. Find the difference between the y coordinates, Δy is change in y.Here you need to know the coordinates of 2 points on a line, (x 1, y 1) and (x 2, y 2).
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