# Mastering the Slope-Intercept Form: A Guide with Examples

The slope intercept form is an important concept used in the coordinate plane to determine the equation of a straight line. The slope intercept form explores the relationship between the variables (unknowns) in the equation.

It is an easy task to determine the equation of a straight line for the value of x (independent variable). In this article, we will describe the concept of the slope intercept form. We will address its definition and formula, as well as some examples.

## Slope Intercept Form

The slope intercept form is an important concept in mathematics that helps us understand and describe linear relationships between two variables. The slope intercept form is an essential relation used to derive the equation of a straight line from the given values. It is a linear equation written as

y = mx + b

In this equation:

• y is the dependent variable (unknown)
• m is the slope of the line
• x is an independent variable
• b is the intercept

The slope elaborates on the steepness (inclination) of a line. While the y intercept elaborates on how a line changes horizontally and vertically, it also provides a precise and concise way to explain the relationship between dependent and independent variables.

Note: The slope intercept form is confined to linear relationships, which may not properly express particular
complex systems.

### The Role of m and b

The slope m determines the steepness of the line and shows the rate of change in y concerning x while the y intercept b lays the point where the line touches the vertical axis when x equals zero.

#### Graphical Representation:

Plotting Points: To apprehend the slope intercept form visually. It is essential to apprehend how to plot points on a graph and sketch lines based on the equation.

Compute the Slope: The slope m can be computed using the formula (change in y) over (change in x) between
two points on the line.

#### Solving Equations:

Single Variable Solving: The slope intercept form simplifies solving linear equations for a single variable.

Systems of Equations: It also plays an essential role in solving systems of linear equations involving multiple
variables.

### Examples of Slope Intercept Form

Here we will address different important cases with examples to improve our understanding of the concept of the slope intercept form.

Case 1. If Two Points are Known:
Example:
Determine the equation of the straight line using the concept of slope intercept form using the following two points:

(11, 13) and (15, 17)
Solution:
Step 1: Given information:
x 1 = 11 and x 2 = 13
y 1 = 15 and y 2 = 17

Step 2: Compute the value of m for the line:
m = 𝚫y/𝚫x = (y2 – y1) / (x2 – x1)
m = (17 – 13) / (15 – 11)
m = 4 / 4
m = 1

Step 3: Compute the value of b i.e. y intercept employing the value of m = 1 and one point from the given two points in the slope intercept formula.
y = mx + b
13 = (4) x (11) + b ……. [using (8, 9)]
13 = 44 + b
13 – 44 = b
– 31 = b
b = – 31

Step 4: Now place the values of m and b in the slope intercept form.
y = mx + b
y = (1)x + (- 31)
y = x – 31

Case 2. If Gradient and Y Intercept are Known:
Example:
Determine the equation of the straight line if the m is – 4 and the b (y intercept) is – 7.
SOLUTION:

Step 1: Given information:
m = – 4 and b = – 7

Step 2: Use the relation of the slope intercept form to find the equation of the straight line.
y = mx + b

Step 3: Now place the values in the formula and simplify.
y = (- 4) x + (- 7) = – 4x – 7

Case 3: If Gradient and One Point Given:
Example:
Determine what the equation of a straight line will be if m = – 9 and the point is (18, 14).
Solution:

Step 1: Given data
Here
m = – 9
x = 18 and y = 14

Step 2: Now determine the value of b using the given point (18, 14) and the value of m = – 9 in the slope intercept form:
y = mx + b
14 = (- 9) x (18) + b
14 = (- 162) + b
14 + 162 = b
b = 176 (y intercept where the line touches the vertical axis)

Step 3: We will place these values of m and b in the slope intercept form:
y = mx + b
y = (- 9) x + (176)
y = – 9x + 176

Wrap Up
The concept of slope intercept form plays an important role in working with linear relationships in mathematics and other disciplines. We have discussed the concept of the slope intercept form in this article. We have elaborated on its definition, including the role of m and b in determining the linear equations, along with examples.

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