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 = 7x - 9 becomes 7x - y = 9 written in standard form. Subtract y from both sides of the equation to get 7x - y - 9 = 0Īdd 9 to both sides of the equation to get 7x - y = 9 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). Drawing a line between (0,7) and (1,9) therefore yields the graph of the straight line y = 2x 7.\\ Knowing this allows us to count 2 units up from (0, 7) and one unit right, which lands us on the point (1, 9). Since slope is we know that for every 2 units that the line increases, it traverses 1 unit in the x direction. Thus, to graph the line, all we have to do is apply the slope formula. We know one point on the line, (0, 7), because the y-intercept is given. Slope-intercept form is often used when introducing linear equations because it very quickly gives us information that we can use to graph the line. In this linear equation, the slope of the line is 2, and the y-intercept occurs at (0, 7). The slope and the y-intercept can be any real number. In other words, the y-intercept occurs at x = 0. The y-intercept occurs at the point where the line crosses the y-axis. Where m is the slope and b is the y-intercept of the line. A linear equation in slope-intercept form takes the following form: Slope-intercept form is one of a number of forms that linear equations take. Thus, given an equation of a line, if we can convert the equation to either of the forms described above, we can simply read off m to determine the slope. In both of these formulas, m represents the slope of the line. ![]() For example, there are a few different forms for the equation of a line, such as slope intercept form and point slope form. There are also other ways to find the slope. If we are instead given a graph of a line on a coordinate plane, simply pick two points on the line, then start at one point and count the number of units you need to move vertically and horizontally to get to the other point the number of units in the vertical direction is the change in y, the number of units in the horizontal direction is the change in x, and the slope is the change in y over the change in x. How to find the slope of a line?įinding the slope is relatively straightforward given two different points on a straight line, as shown in the example above. However, if we were to have subtracted 4 from 1, but then subtracted 3 from 2 instead in the first example, the slope would have been 3 rather than -3, which is incorrect. Notice that in either case, the result is the same. ![]() For example, given the points (3, 1) and (2, 4), the slope of the line can be calculated as follows: 1 - 4 Note that it does not matter which value is subtracted from the other, as long as the points used are consistent for both y and x. Similarly, subtract the x-value one point from the x-value of another. Given two different points on a line, the change in y is calculated by subtracting the y-value of one point from the y-value of the other point. The slope formula is simply the change in y over the change in x: Slope = m = Given two different points on a line, it is relatively simple to calculate the slope of the line using the slope formula. If the slope is negative, then the line decreases as it proceeds from left to right. If the slope is positive, then the line increases as it proceeds from left to right. If the slope is 0, that means that the line is a horizontal line. The slope of a line can either be positive or negative. ![]() ![]() It is often described as because it tells us how many units the line increases in the vertical direction (rise) over a given change in the horizontal direction (run). The slope of a straight line is a measure of the steepness of the line. To use the calculator, please provide the coordinates of two different points and click the "Calculate" button. It also provides a diagram of the line, as well as determines the angle the line forms with respect to the x-axis. Given the coordinates of two different points on a line, this slope calculator can be used to find the slope and equation of the line.
0 Comments
Leave a Reply. |