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How To Find Equation in Slope Intercept Form?
The slope-intercept form is the most common form of a line. Many people find this beneficial because of its intelligibility.
Anybody can easily express the characteristics of the line even without checking its graph because the y-intercept and the slope can easily be identified from the straight line.
The slope intercept form calculator determines the equation of a straight line from the two different points that this particular line passes through.
These calculators also help to find the x-intercept, y-intercept, and coefficients of slope using slope-intercept formulas.
What is a slope intercept form?
A straight line on a plane can be expressed mathematically as a relationship among the horizontal (x-axis) and vertical (y-axis) positions of every point that subscribes to the line.
The relationship between different positions of each of the points can be written as x = [y with other value].
The particular form of [y with other value] will tell what type of line we have. For instance, x = y_{2} + y is a parabola, also described as quadratic function.
So, there are many ways to write the equation of a line. But one of the most popular methods is called slope-intercept form and the slope intercept form calculator identifies the slope and the y-intercept. Apart from this y = mx + b is the relationship of a straight line where the slope is the number (m) written just before the x and the y-intercept is a constant which is written at the end.
Mostly, y-intercept calculators will focus on a straight line so, linear equations or line equations can be instantly realized as they have no expressions with exponents in them.
For instance, you will determine an “a” or a “b”, but never a^{2}. Each linear equation state a line, which can be expressedwith the slope intercept form equation.
The term slopes are the gradient or incline of a straight line. It describes how much y transforms for a fixed change in x. If it is negative (–ve) then y decreases with an increasing x. Conversely, if it is positive (+ve) then the value of y increase with the value of x.
In yintercept calculator to find to the value of y at which the straight line crosses the y-axis, you have to plug x = 0 in the linear equation.
Slope-intercept formula:
If you know two points that the line goes through. The first point will have coordinates (x_{1}, y_{1}) and the second point will have (x_{2}, y_{2}). The unknown values are the slope (m) and the y-intercept (b).
First of all, add the coordinates of the points into the slope intercept equation:
y_{1} = mx_{1} + b
y_{2} = mx_{2} + b
Now, subtract the first equation from the second equation:
y_{2} – y_{1} = m(x_{2}– x_{1})
Then, to find the slope, divide by (x_{2} – x_{1}) both sides of equation:
(y_{2} – y_{1})/ (x_{2}– x_{1}) = m(x_{2}– x_{1})/(x_{2}– x_{1})
m = (y_{2} – y_{1})/ (x_{2}– x_{1})
Once you find the slope, you can add it into any first or second equation for y-intercept:
y_{2} = x_{2} (y_{2} – y_{1})/ (x_{2}– x_{1}) + b
b = y_{2} – x_{2} (y_{2} – y_{1})/ (x_{2}– x_{1})
An online slope intercept form calculator uses these equations to find all intercept points.
Example:
Write the equation of the straight line through the points (8, 13) and (12, 22)
- Find the slope (m).
Use the straight line formula to calculate the slope between the two points.
m = 22 – 13/ 12 – 8= 9 /3 = 3
Once you figure out the slope, substitute it in for “m” in y = mx + b. This provides y = 3x + b.
- Find the b (y-intercept)
Choose one point on the line and use the values of x and y to calculate b. It does necessarily which point you choose.
We’ll select the first point (8, 13) and substitute in 8 for x and 13 for y. You can add these values in the y intercept calculator to solve the b otherwise use the pointto solve for the b(y-intercept).
13 = 3(8) + b
By multiplying
13 = 24 + b
Now, simplify and solve for b.
b = 13-24
b = -11
- Write formula in the slope-intercept form: (y = mx + b)
Now we know the values of b = -11 and m = 3, we can add these values and write the equation in slope-intercept form.
y = 3x – 11
- Verify the answer
We used the points (4,7), so to verify our equation we require to use the other points such as (6,13). If you utilize the same points twice, it will not find an error. Ensure to use the point you didn’t already use to determine the b in the earlier steps.
Substitute the x value from another point and check if it works. If we add 6 as the value of x in our equation, then the value of y should come out to 13.
3(6) – 11 = 18 – 11 = 7.
How to find the equation in slope-intercept form?
To determine the equation of a straight line in the slope-intercept form. You simply add the given values in slope intercept form calculator otherwise all you have to provide two points that the straight line goes through. You require to follow the technique outlined below.
Write the coordinates of the initial point. Let’s suppose it is the point with x₁ = 3 and y₁ = 17.
Now, write the coordinates of the other point as well. Let’s assume the point value is x₂ = 6 and y₂ = 23.
Use the slope intercept formula to determine the slope which formula is used by y intercept calculator:
m = (y₂ – y₁)/(x₂ – x₁)
m = (23-17)/(6-3) = 6/3
m = 2
Compute the y-intercept. You can also use the points x₂ and y₂ instead ofy₁ and x₁ here.
b = y₁ – m * x₁
By substituting the value of m in the equation
b = 1 – 2*1 =
b = -1
Put all values together to build the slope intercept form of the linear equation:
y = 2x – 1.
How find the x and y-intercept?
To compute the x-intercept of a straight line. It is the value of x at which the line crosses the x-axis you can calculate it with slope intercept form calculator and with the following process:
0 = mx + b
x = -b/m
Hence, an online y interceptcalculator will provide both values of x and y-intercept 100% accurately in a fraction of a second.