Hi Using the point-slope formula, (0, 5) and (�2, 11) m = -6/2 = -3 Using the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. y = -3x + b 5 = -3*0 + b 5 = b y = -3x+5
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The equation is useful when we know:
and want to find other points on the line. Have a play with it (move the point, try different slopes): Now let's discover more. What does it stand for?(x1, y1) is a known point m is the slope of the line (x, y) is any other point on the line It is based on the slope: Slope m = change in y change in x = y − y1 x − x1
So, it is just the slope formula in a different way! Now let us see how to use it.
slope "m" = 31 = 3 y − y1 = m(x − x1) We know m, and also know that (x1, y1) = (3, 2), and so we have: That is a perfectly good answer, but we can simplify it a little: y − 2 = 3x − 9 y = 3x − 9 + 2 y = 3x − 7
m = −3 1 = −3 y − y1 = m(x − x1) We can pick any point for (x1, y1), so let's choose (0,0), and we have: y − 0 = −3(x − 0) Which can be simplified to:
What is the equation for a vertical line? In fact, this is a special case, and we use a different equation, like this: Every point on the line has x coordinate 1.5, What About y = mx + b ?You may already be familiar with the y=mx+b form (called the slope-intercept form of the equation of a line). It is the same equation, in a different form! The "b" value (called the y-intercept) is where the line crosses the y-axis. So point (x1, y1) is actually (0, b) and the equation becomes:
Start withy − y1 = m(x − x1) (x1, y1) is (0, b):y − b = m(x − 0) Which is:y − b = mx Put b on other side:y = mx + b 519, 521, 522, 1160, 1161, 1162, 2074, 2075, 9027, 9028, 9029 Copyright © 2022 Rod Pierce 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 ! |