The Slope-Intercept Formula By now, you’ll want to cut to the chase and find the slope-intercept form of a linear equation. You will learn more about that below, including the importance of this rule in linear equations. In a linear equation, you find it by substituting x for 0 (x = 0). It crosses the straight line at the y-axis. If the difference in x is positive, y increases. It determines any changes in y due to a fixed shift in x. The slope part refers to a gradient or incline. These values come in handy for linear interpolation. You learn the slope is m and the y-intercept is b. The slope-intercept form has an equation that looks like y = mx + b, as mentioned before. A linear equation describes a straight line, using a slope-intercept form to express it. You will see an x and y, but you won’t see an x2 or y2. Straight line equations, or linear equations, have no terms with exponents. You can use a parabola calculator to learn more about that side of things. With this slope intercept form calculator, you work with the straight line. ![]() The relationship of a straight line (with b and m as numbers) are y = mx + b. An example of that would be the quadratic function – y = x2 + x, which is a parabola. What goes with x determines the line you have. Both are points that contribute to that line. Definition of Slope-Intercept Form You can describe a line in a flat plane as having an X and Y axis. Read on to discover more about slope intercept formulas, linear equations, and more. This tool lets you find the x and y-intercepts and the coefficients of the slope. 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.Do you need to find an equation for a line that passes through two points? It might seem challenging, but a slope intercept form calculator can help. 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. ![]() 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. 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.
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