This form is known as the Slope Intercept Form and it is a most useful form as it immediately shows two important things about any straight line when graphed on a Cartesian plane; the slope m, and the y-intercept b. There are other forms of the equation of a straight line and the examples below will show how to convert from these to the slope intercept form. There is more here on the slope of a line so we will start by looking at the y-intercept. The y-intercept The y-intercept is the point at which a straight line intersects the y-axis.
Let's first quickly review slope intercept form. Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information.
All you need to know is the slope rate and the y-intercept. Continue reading for a couple of examples! Writing an Equation Given the Slope and Y-Intercept Write the equation for a line that has a slope of -2 and y-intercept of 5.
I substituted the value for the slope -2 for m and the value for the y-intercept 5 for b. The variables x and y should always remain variables when writing a linear equation. In the example above, you were given the slope and y-intercept. Now let's look at a graph and write an equation based on the linear graph.
Locate another point that lies on the line. Calculate the slope from the y-intercept to the second point. Write an equation in slope intercept form given the slope and y-intercept.
You can also check your equation by analyzing the graph. You have a positive slope. Is your graph rising from left to right? Yes, it is rising; therefore, your slope should be positive!
We've now seen an example of a problem where you are given the slope and y-intercept Example 1. Example 2 demonstrates how to write an equation based on a graph. Let's look at one more example where we are given a real world problem. How do we write an equation for a real world problem in slope intercept form?
What will we look for in the problem? Real World Problems When you have a real world problem, there are two things that you want to look for! The rate is your slope in the problem.
The following are examples of a rate:Writing linear equations using the slope-intercept form. Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.
We've got a value for m and a value for b. In many cases the value of b is not as easily read. The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x: y = a + bx.
b is the slope. a is a constant timberdesignmag.com is the y intercept, the. How Do You Write the Equation of a Line in Slope-Intercept Form If You Have a Graph?
Write an equation in slope-intercept form for Trying to find the equation . The slope-intercept form of the equation of the line that passes through the points (5,-1) and (2,-7) is y = 2x - To find this equation, we must first be familiar with two forms of an equation.
Write an equation in slope-intercept form for each graph shown.
62/87,21 You need to find the slope and y-intercept to write the timberdesignmag.com line crosses the y-axis at (0, 7), so the y- intercept is 7. y=mx+by = mx + by=mx+b. This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept.
(For a review of how this equation is used for graphing, look at slope and graphing.) I like slope-intercept form the best.