This calculator will find the equation of a line (in the slope-intercept, point-slope, and general forms) given two points or the slope and one point, with steps shown. Show Related calculators: Slope Calculator, Parallel and Perpendicular Line Calculator SolutionYour input: find the equation of a line given two points $$$P=\left(-4, 7\right)$$$ and $$$Q=\left(1, 2\right)$$$. The slope of a line passing through the two points `P=(x_1, y_1)` and `Q=(x_2, y_2)` is given by `m=(y_2-y_1)/(x_2-x_1)`. We have that $$$x_1=-4$$$, $$$y_1=7$$$, $$$x_2=1$$$, $$$y_2=2$$$. Plug the given values into the formula for slope: $$$m=\frac{\left(2\right)-\left(7\right)}{\left(1\right)-\left(-4\right)}=\frac{-5}{5}=-1$$$. Now, the y-intercept is `b=y_1-m*x_1` (or `b=y_2-m*x_2`, the result is the same). $$$b=7-\left(-1\right) \cdot \left(-4\right)=3$$$. Finally, the equation of the line can be written in the form `y=mx+b`. $$$y=-x+3$$$. Answer: The slope of the line is $$$m=-1$$$. The equation of the line in the slope-intercept form is $$$y=-x+3$$$. The equation of the line in the point-slope form is $$$y - 7 = - (x + 4)$$$. The equation of the line in the point-slope form is $$$y - 2 = - (x - 1)$$$. The general equation of the line is $$$x + y - 3 = 0$$$. Created by Julia Żuławińska Reviewed by Steven Wooding Last updated: Apr 06, 2022 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. What is a slope?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:
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. What is the point-slope form?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:
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:
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:
In the two graphs below, you can see the same function, only described with two different forms of a linear equation: How to find the equation of a line with slope and coordinates of a point?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.
💡 If you need to find a different point on your line click on the And here you have it! We hope you enjoyed our point-slope form calculator! Before you go, check out more of our geometry calculators! Average rate of changeBilinear interpolationCatenary curve… 35 more |