When it comes to algebra, one of the most important concepts is graphing linear equations. To graph a linear equation, it is essential to write it in slope-intercept form.
The slope intercept form is a way of writing an equation in the form y=mx+b, which tells us the slope of the line (m) and the y-intercept (b).
Read on to explore everything you need to know about the slope intercept form, how it works, and its applications in real-life situations.
What is Slope Intercept Form?
Slope intercept form is a way to represent a linear equation on a graph. It is also known as y = mx + b, where ‘m’ is the slope of the line and ‘b’ is the y-intercept.
- The slope is the ratio of the change in the y-coordinate to the change in the x-coordinate, also known as rise over run.
- The y-intercept is the point where the line intersects with the y-axis.
Simply put, slope intercept form enables us to determine the equation of a line from just its slope and y-intercept. In other words, a slope intercept form is used to represent a linear equation in a very simple way.
How to Find the Slope
Slope intercept form is also known as y = mx + b, where ‘m’ is the slope of the line and ‘b’ is the y-intercept. The slope (m) describes how steep the line is.
To find the slope of a line in slope intercept form:
- Simply look at the coefficient of x (m).
- If the coefficient is positive, the line will go up from left to right.
- And if it is negative, the line will go down from left to right.
- Additionally, the larger the coefficient is, the steeper the line will be.
How to Find the Y-Intercept
The y-intercept (b) is the point where the line crosses the y-axis. To find the y-intercept of a line in slope intercept form:
- You need to look at the constant term (b).
- The y-intercept is the point (0, b) on the graph, and it represents the value of y when x is equal to zero.
Examples of Graphing Linear Equations in Slope Intercept Form
Let’s say you have the equation y=3x+2. To graph this equation:
- Start by plotting the y-intercept (0,2) on the y-axis.
- Then, use the slope (3) to find a second point.
- Then use the T table; for example, if x = 1, then y = 5, which will give you the point (1,5).
- Plot this point and draw a line through the two points to graph the equation.
Real-Life Applications of Slope Intercept Form
One of the key applications of slope intercept form is in graphing linear equations. By knowing the slope and y-intercept of a line, we can easily plot it on a graph and find out its direction and orientation. This information can be useful in determining the relationship between two variables in a real-life situation.
For example, if we want to know the relationship between the quantity and the price of a product, we can use slope intercept form to graph this relationship and find out if it is a positive or negative correlation.
Another important application of slope intercept form is in the field of economics because many economic relationships are linear in nature and can be represented by a straight line.
For example, the relationship between income and spending can be represented by a linear equation, where the slope represents the marginal propensity to consume (MPC), measuring how much more consumers will spend for every additional dollar of income, and the y-intercept represents autonomous spending. By using slope intercept form, economists can easily analyze and predict the behavior of consumers and businesses.
What to read next:
- Finding the Equation of a Tangent Line with Derivatives.
- Solving Systems of Equations by Substitution Method.
- 9 Best YouTube Channels to Learn Calculus.
The slope intercept form is an essential tool for graphing linear equations. It is a simple and effective way to write an equation that tells you the slope and y-intercept of the line.
Whether it is graphing linear equations, finding the equation of a line, or analyzing economic relationships, understanding the basics of slope intercept form is essential.