If you know the slope m of a line and the coordinates (x1,y1)(x1,y1) of one point on the line, you can write the equation of the line in point-slope form which is nothing but y−y1=m(x−x1). Learn more about Point slope Continue reading →. Start with the 'point-slope' formula (x 1 and y 1 are the coordinates of a point on the line): y − y 1 = m(x − x 1 ) We can choose any point on the line for x 1 and y 1, so let's just use point (2,3).
- Point Slope Formula To Slope Intercept
- Pt Slope Formula Example
- Point Slope Formula Calculator Graph
- Point Slope Formula Calculus
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Point of Intersection Formula
Have you heard of point of intersection concept in mathematics? If no, don't panic. Here, we will discuss the point of intersection in detail and how to calculate it either graphically or algebraically. Also, the formula is applicable to a variety of areas like businesses, finance, study, construction, or physics etc.
Have you ever noticed the traffic signal on a road? This is the example of point of intersection that will appear at the point when two roads are meeting up at a point. In mathematics, point of intersection is the point where two lines or curves generally meet.The value of two curves would be same significantly and it can be used at multiple places.
Take another example, if we wanted to represent the revenue of a Company against the costs then point of intersection would define the situation where revenue and costs are significantly the same. Most of the times, this is the breakeven point for a Company. The point can be calculated either graphically or algebraically.
Draw the graph of two equations and see where they will intersect visually. This is not a tough job but can be completed quickly with a deep understanding and practice. In most of the examples, you could analyze that graph is the best technique to find the point of intersection with accuracy.
Sometimes, there are the situation when this is not possible to find the point of intersection graphically then how can you solve the equation. The answer is you can do it algebraically. Solve the equations find the values of x coordinated that would point of intersection for both the equations.
Point Gradient Formula
For a line, the ratio of vertical change to the horizontal change is defined through a point i.e. named as the point of gradient or we can name it as the derivative as well. In brief, the gradient of a line will be rise divided by the run – rise/run. If m is the gradient point across a line then point gradient formula in mathematics could be given as –
[large Point;Gradient =frac{y-y_{1}}{x-x_{1}}]
Point Slope Form Formula
The other popular format for straight line equations is point slope formula. For this purpose, you need to find out the values (x1, y1) and a slope m. Further, plug the values into the formula –
[large y-y_{1}=m(x-x_{1})]
Where,
m is the slope of the line.
x1 is the co-ordinates of x-axis.
y1 is the co-ordinates of y-axis.
Don't scare of subscripts but they are just intended to indicate the points given to you. If you have the generic values for x and y coordinates then it can be directly plugged into the formula to calculate the final output. If you will calculate the values calculated from the slope-intercept form and the point slope form then they are exactly the same.
So, this is your choice which method are you planning to use and which technique suits you the most. Practice the technique and apply it as per your convenience for next mathematics problem.
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Let's say we were given two points on a line, say (-4, -7), and (12, 1), and we wanted to determine the equation of a line. We would have an interesting situation because the point-slope formula requires both a point and a slope. We have a point, but we have no slope.
In order to use the point-slope formula, we will first have to calculate the slope of the line. Here is the equation for slope, called ‘m.'
Don't let the subscripts confuse you. The subscripts, the little numbers at the bottom of the letters, mean the letters are numbered. We are talking about a formula that requires two points.
The two points are generically written as (x1, y1) and (x2, y2) for the purposes of the formula. So, we have to decide which of our given points is the first point and which is the second point. It is an arbitrary decision and the answer we be the same regardless.
Let us use (-4, -7) as (x1, y1) and (12, 1) as (x2, y2). Let us substitute the values into our slope formula.
This fraction can be reduced. Left to the reader, the reduced fraction is this.
Now that we have a slope, we can use the point slope formula. Our last decision will be which of our two points to use. Do we use (-4, -7) or (12, 1)? Again, it is an arbitrary decision. We can use either point and we will get the same equation of the line. Let's use (-4, -7) so we can practice using negative numbers.
Let's substitute our point and our slope into the point-slope formula. First, we will insert the slope, 1/2.
Next, we will place in our point, (-4, -7). Remember, the x-value is -4 and the y-value is -7.
We can cancel the double negatives, because the opposite of a negative number is a positive number.
Next, we will do the distributive property and multiply everything in the parentheses by 1/2.
Let's multiply the 1/2 and the 4. Doing so, we get 2.
Point Slope Formula To Slope Intercept
Last, we will subtract 7 from both sides of the equation to isolate the ‘y.'
Pt Slope Formula Example
Here is the final equation of the line.
Point Slope Formula Calculator Graph
Now, test your own skills with a problem of your own. Use the interactive quiz to try a problem.
Point Slope Formula Calculus
ideo: The Point-Slope Formula: Given Two Points
uiz: The Point-Slope Formula: Given Two Points
