The 'point-slope' form of the equation of a straight line is:
The equation is useful when we know:
- one point on the line: (x1,y1)
- and the slope of the line: m,
and want to find other points on the line.
Write in point-slope form the equation of a line with a slope of 7 containing the point (8, 5). This is a page from the dictionary MATH SPOKEN HERE!, published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1. You are hereby granted permission to make ONE printed copy of. Equation from 2 points using Point Slope Form. As explained at the top, point slope form is the easier way to go. Instead of 5 steps, you can find the line's equation in 3 steps, 2 of which are very easy and require nothing more than substitution! In fact, the only calculation, that you're going to make is for the slope. Write in point-slope form the equation of a line with a slope of 7 containing the point (8, 5). This is a page from the dictionary MATH SPOKEN HERE!, published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1.
Have a play with it first (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
Making sense of it
It is based on the slope:
Slope m = change in ychange in x = y − y1x − x1
Starting with the slope: we rearrange it like this: to get this: |
So, it is just the slope formula in a different way!
Now let us see how to use it.
Example 1:
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
Example 2:
m = −31 = −3
y − y1 = m(x − x1)
Free slots play 999. We can pick any point for (x1, y1), so let's choose (0,0), and we have:
Point Slope Format
y − 0 = −3(x − 0)
Point Slope Form To Slope Intercept Form
Which can be simplified to:
Example 3: Vertical Line
What is the equation for a vertical line?
The slope is undefined!
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,
that's why its equation is x = 1.5
What About y = mx + b ?
The 'point-slope' form of the equation of a straight line is:
The equation is useful when we know:
- one point on the line: (x1,y1)
- and the slope of the line: m,
and want to find other points on the line.
Write in point-slope form the equation of a line with a slope of 7 containing the point (8, 5). This is a page from the dictionary MATH SPOKEN HERE!, published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1. You are hereby granted permission to make ONE printed copy of. Equation from 2 points using Point Slope Form. As explained at the top, point slope form is the easier way to go. Instead of 5 steps, you can find the line's equation in 3 steps, 2 of which are very easy and require nothing more than substitution! In fact, the only calculation, that you're going to make is for the slope. Write in point-slope form the equation of a line with a slope of 7 containing the point (8, 5). This is a page from the dictionary MATH SPOKEN HERE!, published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1.
Have a play with it first (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
Making sense of it
It is based on the slope:
Slope m = change in ychange in x = y − y1x − x1
Starting with the slope: we rearrange it like this: to get this: |
So, it is just the slope formula in a different way!
Now let us see how to use it.
Example 1:
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
Example 2:
m = −31 = −3
y − y1 = m(x − x1)
Free slots play 999. We can pick any point for (x1, y1), so let's choose (0,0), and we have:
Point Slope Format
y − 0 = −3(x − 0)
Point Slope Form To Slope Intercept Form
Which can be simplified to:
Example 3: Vertical Line
What is the equation for a vertical line?
The slope is undefined!
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,
that's why its equation is x = 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 at (0, b)
and the equation becomes:
The calculator given in this section from DoMyWriting can be used to find the equation of a line when a point on the line and its slope are given.
Let (x1, y1) be a point on the line and m be the slope of the line.
Blanca ocasio cortez. Then, the formula to find the equation of a line is
y - y1 = m(x - x1)
But, the above equation can be written in the general form as shown below.
ax + by + c = 0
|
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