Find the slope and y intercept of the graph calculator

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Data Points
Number Line
What is slope intercept form?
How to find slope intercept form?
References:
How do you find the slope and y
How do you find slope

Data Points

This Slope and y-intercept Calculator calculates the best-fitting slope and best-fitting y-intercept for a linear line based on the given data points supplied.

So we begin with a few data points.

We create a regression line to build the best-fitting line for the various data points.

A regression line is a line that tries its best to represent all of the data points as accurately as possible with a straight line. It strives to be the best fit line that represents the various data points.

A regression line can be calculated based off of the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between 2 quantitative variables. If data points are perfectly linear, the sample correlation will either be 1 (for a line with a positive slope) or -1 (for a line with a negative slope). All values in between are not linear (with the exception of a vertical line which has a correlation coefficient of 0).

So based off of the sample correlation coefficient, we can determine the calculate the slope and y-intercept of the best-fitting line for these data points.

How we determine the slope of the line is complex for a regression line and is not simply rise/run, as the simple formula is. To find the slope of a regression line (or best-fitting line), the formula is, slope, m= ((1/n-1)∑(x-μx) (y-μy)/σxσy)(σy/σx) Or if we take simplify by putting in r for the sample correlation coefficient, the formula is, slope, m= r(σy/σx)

So once you have computed the correlation coefficient, then calculating the best fit line is relatively simple.

We first calculate the slope through the formula, m= r(σy/σx)

Once we have done this, then we can calculate the y-intercept. We do this by multiplying the slope by x. We then subtract this value from y. This is the y-intercept.

With the slope and y-intercept calculated, we then can have our regression line.

Example

Now that you know the steps to do, let's actually do an example.

So as an example, let's say we have a correlation coefficient of 0.98, x of 7, x of 12, σx of 4.58, and σy of 5.

So to find the slope, we use the formula, m= r(σy/σx)= 0.98(5/4.58)= 1.069

We then need to find the y-intercept. We multiply the slope by x, which is 1.069*7=7.489.

We then subtract this value from y, which is 12-7.489= 4.511

So our final regression line is, y= 1.069x + 4.511

To use this calculator, a user simply enters in the x and y value pairs. A user can enter anywhere from 3 to 10 (x,y) value pairs. After, the user clicks the 'Calculate' and the expected value will be calculated and automatically displayed.

Related Resources

Related » Graph » Number Line » Similar » Examples »

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Examples

y-intercept\:y=\frac{x^2+x+1}{x}
y-intercept\:f(x)=x^3
y-intercept\:f(x)=\ln(x-5)
y-intercept\:f(x)=\frac{1}{x^2}
y-intercept\:y=\frac{x}{x^2-6x+8}
y-intercept\:f(x)=\sqrt{x+3}
y-intercept\:f(x)=\cos(2x+5)
y-intercept\:f(x)=\sin(3x)

y-intercept-calculator

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A Slope intercept is a straight line on the coordinate plane that can be described by the equation y=mx+b, where m is the slope of the line and b is the intercept.

Formula

Slope Intercept Form
y = mx + b

What is slope intercept form?

Slope Intercept Form is also called as gradient, y-intercept form. Slope Intercept Form is used to generate the Equation of a straight line with a slope m and y-intercept c of the line.

How to find slope intercept form?

Examples:

Calculate the equation of the line with slope of 4 and y-intercept 3.
slope m = 4.
b = 3.
Substitute in the formula as :
y = mx + b
y = (4)x + (3)
y = 4x + 3
Equation = 4x + 3 -y

Equation of the Line = 4x -y + 3

References:

Stapel, E. (2020). Straight-Line Equations: Slope-Intercept Form | Purplemath.com
The slope-intercept form of a linear equation (Algebra 1, Visualizing linear functions) – Mathplanet.
Estela, M. (2020). Slope-Intercept Form of a Straight Line (y = mx + b) | ChiliMath.
Slope intercept form. Formula, examples, and practice problems.. Mathwarehouse.com. (2020).

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How do you find the slope and y

Steps for graphing an equation using the slope and y-intercept:.

Find the y-intercept = b of the equation y = mx + b..

Plot the y-intercept. The point will be (0, b)..

Find the slope=m of the equation y = mx + b..

Make a single step, using the rise and run from the slope. ... .

Connect those two points with your line..

How do you find slope

Slope-Intercept Form Calculator The general formula for slope-intercept form is y = mx + b, where m represents the slope of the line, and b represents the y-value of the line's y-intercept.