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
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.
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.
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).
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
FAQs (Frequently Asked Questions)
1. What are the three techniques for graphing equations?
Three methods exist for graphing linear equations. Students have three options
(1) use the slope and y-intercept to find two points, (2) use the slope and y-intercept, or (3) use the x- and y-intercepts.
2. What guidelines apply when graphing functions?
Students must choose x-values and insert them into the equation in order to graph a function. They will obtain a y-value if they enter those values into the equation. Their coordinates for a single point are made up of their x-values and y-values. Students can learn more about this topic with the aid and assistance of quality reference materials available on the Extramarks learning portal.