The 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. Show 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
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.
\( m = \dfrac {14} {2} \) Line Equations with SlopeThere are 3 common ways to write line equations with slope:
Point slope form is written as 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: 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 Take the point slope form equation and multiply out 7 times x and 7 times 2. 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: Standard form of the equation for a line is written as 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. 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. 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 The point-slope form calculator will show you how to find the equation of a line from a point on that line and the line's slope. Soon, you will know what is point-slope form equation, and learn how is it different from the slope-intercept form equation. We also came up with two exercises, and we'll explain how to solve them in the last paragraph.
Let's start with the basics. What is the slope? The slope, also known as the gradient, is the marker of a line's steepness. If it's positive, it means the line rises. If it's negative - the line decreases. If it's equal to zero, the line is horizontal. You can find the slope between two points by estimating rise over run - the difference in height over a distance between two points. So, slope formula is: m = change in y / change in x = (y - y₁) / (x - x₁) The point-slope form equation is a rearranged slope equation. To find the gradient of non-linear functions, you can use the average rate of change calculator. 🙋 For more information go to the slope calculator.
There is more than one way to form an equation of a straight line. Point-slope form is a form of a linear equation, where there are three characteristic numbers - two coordinates of a point on the line, and the slope of the line. The point slope form equation is: y−y1=m⋅(x−x1)\small y - y_1 = m \cdot (x - x_1)y−y1=m⋅(x−x1) ,where:
Do you see the similarity to the slope formula? What you might not know is that it's not the only way to form a line equation. The more popular is the slope intercept form: y=m⋅x+b\small y = m \cdot x + b y=m⋅x+b ,where:
The truth is that this is nothing else than a more precise point-slope form. A straight line intercepts the y-axis in a point (0, b). If you choose this point - (0, b), as a point that you want to use in the point-slope form of the equation, you will get: y−b=m⋅(x−0)\small y - b = m \cdot (x - 0)y−b=m⋅(x−0), which is the same as y=m⋅x+b\small y = m \cdot x + by=m⋅x+b. In the two graphs below, you can see the same function, only described with two different forms of a linear equation: To learn how to find the x-intercept and y-intercept of a line, visit our x- and y-intercept calculator.
Let's have a look at two exercises, to understand the topic more clearly. The slope of a line is 2. It passes through point A(2, -3). What is the general equation of the line?
Let's solve an exercise with a more relatable subject. Let's say you got a puppy. When you got him he was 14 pounds. It grew 0.2 pounds every day, and after 30 days, he was 20 pounds. Find the general equation of the puppy's growth.
y−20=0.2∗(x−30)\small y - 20 = 0.2 * (x - 30)y−20=0.2∗(x−30) 4. Simplify the equation to get the general equation: 0=0.2x−y+14\small 0 = 0.2x - y + 140=0.2x−y+14 💡 If you need to find a different point on your line click on the advanced mode button. Then, input one coordinate, and get the other. And here you have it! We hope you enjoyed our point-slope form calculator! Before you go, check out more of our ! |