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line-equation-calculator en Calculator UseThe slope of a line is its vertical change divided by its horizontal change, also known as rise over run. When you have 2 points on a line on a graph the slope is the change in y divided by the change in x. The slope of a line is a measure of how steep it is. Slope Calculator SolutionsInput two points using numbers, fractions, mixed numbers or decimals. The slope calculator shows the work and gives these slope solutions:
You will also be provided with a custom link to the Midpoint Calculator that will solve and show the work to find the midpoint and distance for your given two points. How to Calculate Slope of a LineCalculate slope, m using the formula for slope: Slope Formula\[ m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})} \] \[ m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1} \] Here you need to know the coordinates of 2 points on a line, (x1, y1) and (x2, y2). How to Find Slope of a Line
Δy = y2 - y1 Δx = x2 - x1 m = Δy/Δx Example: Find the SlopeSay you know two points on a line and their coordinates are (2, 5) and (9, 19). Find slope by finding the difference in the y points, and divide that by the difference in the x points.
Δy = y2 - y1 Δy = 19 - 5 Δy = 14 Δx = x2 - x1 Δx = 9 - 2 Δx = 7 \( m = \dfrac {14} {2} \) \(m = 7 \) Line Equations with SlopeThere are 3 common ways to write line equations with slope:
Point slope form is written as y - y1 = m(x - x1) Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point slope form. Lets use a point from the original example above (2, 5), and the slope which we calculated as 7. Put those values in the point slope format to get an equation of that line in point slope form: y - 5 = 7(x - 2) If you simplify the point slope equation above you get the equation of the line in slope intercept form. Slope intercept form is written as y = mx + b Take the point slope form equation and multiply out 7 times x and 7 times 2. y - 5 = 7(x - 2) y - 5 = 7x - 14 Continue to work the equation so that y is on one side of the equals sign and everything else is on the other side. Add 5 to both sides of the equation to get the equation in slope intercept form: y = 7x - 9 Standard form of the equation for a line is written as Ax + By = C You may also see standard form written as Ax + By + C = 0 in some references. Use either the point slope form or slope intercept form equation and work out the math to rearrange the equation into standard form. Note that the equation should not include fractions or decimals, and the x coefficient should only be positive. Slope intercept form: y = 7x - 9 Subtract y from both sides of the equation to get 7x - y - 9 = 0 Add 9 to both sides of the equation to get 7x - y = 9 Slope intercept form y = 7x - 9 becomes 7x - y = 9 written in standard form. Find Slope From an EquationIf you have the equation for a line you can put it into slope intercept form. The coefficient of x will be the slope. ExampleYou have the equation of a line, 6x - 2y = 12, and you need to find the slope. Your goal is to get the equation into slope intercept format y = mx + b
How to Find the y-InterceptThe y-intercept of a line is the value of y when x=0. It is the point where the line crosses the y axis. Using the equation y = 3x - 6, set x=0 to find the y-intercept. y = 3(0) - 6 y = -6 The y-intercept is -6 How to Find the x-InterceptThe x-intercept of a line is the value of x when y=0. It is the point where the line crosses the x axis. Using the equation y = 3x - 6, set y=0 to find the x-intercept. 0 = 3x - 6 3x = 6 x = 2 The x-intercept is 2 Slope of Parallel LinesIf you know the slope of a line, any line parallel to it will have the same slope and these lines will never intersect. Slope of Perpendicular LinesIf you know the slope of a line, any line perpendicular to it will have a slope equal to the negative inverse of the known slope. Perpendicular means the lines form a 90° angle when they intersect. Say you have a line with a slope of -4. What is the slope of the line perpendicular to it?
Further StudyBrian McLogan (2014) Determining the slope between two points as fractions, 10 June. At https://www.youtube.com/watch?v=Hz_eapwVcrM How do you find the line that passes through points?Steps to find the equation of a line from two points:. Find the slope using the slope formula. ... . Use the slope and one of the points to solve for the y-intercept (b). ... . Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.. How do you find a line that passes through a point with a slope?These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.
What is the slope of the line that passes through the points (The slope of the line passing through the points (-2, 5) and (1, 4) is m = -1/3.
How do you graph a linear equation that passes through two points?Step 1: Find the y-intercept and plot the point. Step 2: From the y-intercept, use the slope to find the second point and plot it. Step 3: Draw a line to connect the two points.
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