A slope-intercept form is a way of stating a linear equation in two variables, usually written as y = mx + c, there where m denotes the slope of the line and c denotes the y-intercept.

Now other words, a slope-intercept form defines the relationship between the variables x and y in a linear equation, there where the slope denotes a rate of change of y to x, and the y-intercept denotes the value of y when x is equal to zero.

In this article, we will discuss the basic definition with the equation, and explanation of the topic with the help of examples.

Explanation

## What is slope-intercept form?

The slope intercept form is a widely used equation format in mathematics to denote the equation of a straight line. The linear equation can be written as

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line. A slope (m) is the ratio of the change in y over the change in x, or the rise over run, which denotes the steepness of the line. Now, the y-intercept (c) is the point where the line intersects the y-axis.

Using the slope-intercept form, we can easily graph a linear equation and determine important properties such as the slope, y-intercept, and x-intercept. The purpose of this equation is straightforward.

To calculate the slope-intercept form of a straight line, we would need the slope-intercept form the inclination angle of this straight line from the x-axis, and the intercept that it makes with the y-axis. A slope-intercept formula cannot be applied to calculate the equation of a vertical line. For example to understand the application of the slope-intercept formula.

#### Basic Rule of the Slope Intercept Form:

The line may have a negative slope in a method the angle it makes with the positive x-direction is obtuse. The value of tan θ, in this method, will be negative, so m will be negative.

To line passing through the origin, the y-intercept will be (c = 0), so its equation will be y = mx.

#### The Straight-Line Equation Using Slope Intercept Form:

We would need two quantities to calculate the equation of a line with an inconsistent aptitude. The inclination of the line or angle, θ, it makes with say, the x-axis, and the placement of the line. Where the line passes through regarding the axes.

Now, we can specify the placement of the line by specifying the point on the y-axis through which the line passes. In general, specifying the y-intercept c.

#### Steps to calculate the equation of a line using the slope-intercept form:

**Step 1: **

Note down the y-intercept c, and the slope of the line as m. If the slope of the line is not given then it can be calculated either with the help of slope formula or a slope calculator.

**Step 2: **

The slope-intercept formula: y = mx + c.

#### For Slope Intercept Form x Intercept:

The slope-intercept formula can be written as form the equation of line L whose slope is m and x-intercept d as:

y = m(x – d)

Here,

m = Slope of the line

d = x-intercept of the line

Sometimes, the slope of a line may be proposed in terms of tangent angle such as:

m = tan θ

#### Examples Of Slope Intercept Form

In this section, explain the slope-intercept form with the help of examples.

**Example 1:**

What is the slope-intercept form of a straight line if ;

Slope = 4

Point = (5,7)

Solution:

**Step 1: **

Find c by putting the point in the general form.

Y = mx + c

7 = (4)(5) + c

7 = 20 + c

7-20 = c

c = -13

**Step 2: **

Make the equation.

Y = mx + c

Y = 4x – 13

**Example 2:**

Write down the equation of the line through (10,5) and (14,13)

**Step 1: **

Find the slope (m). We use the formula to find the slope between the two points (10,5) and (14,13).

m= (y2-y1)/(x2-x1) = (13-5)/(14-10) = 8/4 = 2

we know that

y = mx + c

This gives you

y = 2x + c

**Step 2: **

Find the y-intercept (c).

Pick one of the points on the line and use x and y values to find c. It does not matter which point you chose. we’ll pick the first point (10,5) and 10 for x and 5 for y.

5 = 2(10) + c

5 = 20 + c

C = 5 – 20

C = -15

**Step 3: **

Write the equation in slope-intercept form ( y = mx + c ).

Now we know that m = 2 and c = -15, we can these values in and write the equation in slope-intercept form.

Y = 2x – 15

**Step 4:
**

**Check your answer**

We use points (10,5) in step 2, so to check our equation we need to use the other point (14,13). If you use the same point twice, you will not find mistakes. Make sure to use the point you did not use to find the y-intercept in step 2.

The use x value from the other point and see if it works. If we use 14 for x in our equation, the y value should come out to 13.

2(14) – 15 = 28 – 15 = 13

If we had used 14 and it came out number that was not 13, that would tell us that we had made a mistake somewhere along the way. If this happens to you start by double-checking to make sure you calculate the slope correctly.

#### Summary

Understanding the Slope-Intercept Form is crucial in mathematics. This article has provided a clear definition, thorough explanation, step-by-step instructions, and helpful calculations to help you grasp this fundamental concept.

Whether you’re a student or simply looking to refresh your math skills, mastering the Slope-Intercept Form is a valuable asset.