# Graph Formula

## Graph Formula

After learning the basic method for graphing straight lines, such as charting some points or drawing a line, it is important to discover the corresponding equations. The slope-intercept form of the straight-line equation facilitates graphing. The slope-intercept formula for the straight line passing through the provided points, if there are two points (a1, b1) and (a2, b2), is

y = mx + b

Where b = y-intercept and m = (b2 – b1)/(a2 – a1)

The relationship between two points with respect to which a line is plotted on the graph is given by the Graph Formula, also known as the slope-intercept form of the straight-line equation. Plotting graphs is easy because of the Graph Formula or equation available as a result. The two points of the line are used to create the Graph Formula. The Graph Formula is expressed as y = mx + b. Slope is the variable m. The number of points students travel up and over, or rise over run, is another term for slope. In the Graph Formula, b=y-intercept. The line will cross the y-axis at this location on the graph.

Assuming the two points are (a1, b1) and (a2, b2), the slope-intercept form of the straight line can be calculated using the following Graph Formula:

y = mx + b

Where,

The slope is m.

B is the y-intercept as well.

The specified points also affect the slope (m) in the Graph Formula. Additionally, the slope formula provides the slope.

## What is the slope?

A slope on a graph is a slanted line segment or the steepness of a line. The slope is calculated using the slope formula by dividing the y-intercept value by the x-intercept value.

Mathematically,

Slope (m) equals (b2 – b1) (a2 – a1)

When people travel to any mountainous place, they frequently consider the slope. The act of a snowboarder skewing is known as hitting the hill. The slope of a line on a graph refers to how steep a line is. It is the y-value change to the x-value change ratio. The method above can be used to get the slope given any two supplied points. The slope of a line on a graph refers to how steep a line is. It is the y-value change to the x-value change ratio. The method above can be used to get the slope given any two supplied points.

### Solved Examples on Graph Formula

• Example 1: With a slope of 3 and a y-intercept of 5, write the equation of the line in slope-intercept form.

Solution: Given,

Slope: m 3

b = 5 as the y-intercept

By changing the values of m and b in y = mx + b, y = (-3)x + b, y = -5x + 3

This is the slope-intercept version of the necessary line equation.

• Example 2: Formulate the equation for the slope-intercept line passing through the point and having a slope of 7 (0, -4).

Solution: Given,

Point = (x, y) = Slope = m = 7 (0, -4)

Students are aware that a line’s equation in slope-intercept form is y = mx + b.

Using the values of m, x, and y that are specified,

-4 = 7(0) + b

-4 = 7(0) + b

Consequently, b = -4 = y-intercept.

The line’s equation is, therefore:

y = mx + b

y = 7x – 4