The general formula for slope-intercept form is , where represents the slope of the line, and represents the -value of the line’s -intercept. Show The slope-intercept form of a linear equation makes it easier for us to identify how steep a line is and where it crosses the -axis. ✨ Drag the points on the graph to see how they affect the equation of the line! ✨ When we're given , we first need to find the slope. Then, we can use the slope and one of the given points to solve for the -value of the -intercept and write the equation in slope-intercept form. What is Standard Form?The general formula for the standard form of a linear equation is , where , , and are all integers. We can go from standard form to slope-intercept form by isolating and simplifying: What is Point-Slope Form?The general formula for the point-slope form of a linear equation is , where represents the slope of a line that contains the point (, ). We can go from point-slope form to slope-intercept form by isolating and simplifying: Check out our or explore our and sections to learn more about slope-intercept form and test your understanding. You can also use the Quick Links menu on the left to jump to a section of your choice. You can also use the Quick Links dropdown above to jump to a section of your choice. 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 How do you find an equation in slopeA 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) , which is the same as y = m * x + b .
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