Slope intercept form calculator

Slope intercept calculator is used to find the equation of the line using two points, one point & slope, and y-intercept & slope. This slope intercept equation calculator will give the step-by-step solution to the given problems.

What is the slope intercept form?

A slope intercept form is a specific form of the straight-line equation. The general expression of the slope intercept form is:

y = mx + b

Where,

• x & y are the fixed points of the line.
• “m” is the slope (steepness) of the line.
• “b” is the y-intercept of the line.

The equation of the straight line can be determined with the help of point slope form and the slope intercept form but the slope intercept form is the most accurate and prominent form of the linear equation of the line.

How to find the slope intercept form?

Here are the steps to find the slope intercept form.

• First of all, calculate the slope (m) of the line.
• After that, evaluate the y-intercept (b) of the line.
• Substitute the values of slope and y-intercept of the line to the general expression of the slope intercept form.

Let us take a few examples to learn how to determine the linear equation of the line by using the slope intercept form.

Example 1: For two points

Calculate the linear equation of the line if the given points are (3, -4) & (6, 8).

Solution

Step 1: First of all, take the given points of the line.

X₁ = 3

X₂ = 6

Y₁ = -5

Y₂ = 8

Step 2: Calculate the slope of the line.

Slope = m = y2 – y1 / x2 – x1

Slope = m = 8 – (-4) / 6 – 3

Slope = m = 8 + 4 / 3

Slope = m = 12/3 = 4

Step 3: Now evaluate the y-intercept of the line.

Y = mx + b

-4 = 4(3) + b

b = -4 -12 = -16

Step 4: Now put the slope and y-intercept to the general expression of the slope intercept of the line.

Y = mx + b

Y = 4x + (-16)

Y = 4x – 16  

Example 2: For one point and slope

Calculate the linear equation of the line if the slope of the line is 12 and points are (11, 4).

Solution

Step 1: First of all, take the given slope and the points of the line.

Slope = m = 12

X₁ = 11

X₂ = 4

Step 2: Now evaluate the y-intercept of the line.

y = mx + b

4 = 12(11) + b

b = 4 – 132 = -128

Step 3: Now put the slope and y-intercept to the general expression of the slope intercept of the line.

Y = mx + b

Y = 12x + (-128)

Y = 12x – 128

Example 3: For slope & y-intercept

Calculate the linear equation of the line if the slope of the line is 5 and the y-intercept of the line is -3.

Solution

Step 1: First of all, take the given slope and y-intercept of the line.

Slope = m = 12

y-intercept = b = -3

Step 2: Now put the slope and y-intercept to the general expression of the slope intercept of the line.

Y = mx + b

Y = 12x + (-3)

Y = 12x – 3

References

• what is slope intercept form? Study.com | Take Online Courses. 
• calculating slope intercept form. KATE'S MATH LESSONS. (n.d.).