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!
Slope-intercept form linear equations Video transcript So you may or may not already know that any linear equation can be written in the form y is equal to mx plus b.
Where m is the slope of the line. The same slope that we've been dealing with the last few videos. The rise over run of the line. Or the inclination of the line. And b is the y-intercept. I think it's pretty easy to verify that b is a y-intercept.
The way you verify that is you substitute x is equal to 0. If you get x is equal to remember x is equal to 0, that means that's where we're going to intercept at the y-axis. If x is equal to 0, this equation becomes y is equal to m times 0 plus b. I don't care what m is. So then y is going to be equal to b.
So the point 0, b is going to be on that line.
The line will intercept the y-axis at the point y is equal to b. We'll see that with actual numbers in the next few videos.
Just to verify for you that m is really the slope, let's just try some numbers out. We know the point 0, b is on the line.
What happens when x is equal to 1? You get y is equal to m times 1. Or it's equal to m plus b. So we also know that the point 1, m plus b is also on the line. This is just the y value. So what's the slope between that point and that point? Let's take this as the end point, so you have m plus b, our change in y, m plus b minus b over our change in x, over 1 minus 0.
This is our change in y over change in x.
Sep 09, · This video provides an example of how to determine the equation of a line in slope intercept form given the graph of a line. Graph a Linear Equation in Point-Slope Form Writing Linear. Section Write Equations in Slope Intercept Form A Write an equation of a line when given the graph of the line, a data set, two points on the line, or the slope and a point of the line; A Describe and calculate the slope of a line given a data set or graph of a line, recognizing that the slope is the rate of change;. 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.
We're using two points. That's our end point. That's our starting point. So if you simplify this, b minus b is 0. So hopefully you're satisfied and hopefully I didn't confuse you by stating it in the abstract with all of these variables here.
But this is definitely going to be the slope and this is definitely going to be the y-intercept. Now given that, what I want to do in this exercise is look at these graphs and then use the already drawn graphs to figure out the equation.
So we're going to look at these, figure out the slopes, figure out the y-intercepts and then know the equation.
So let's do this line A first. So what is A's slope? Let's start at some arbitrary point. Let's start right over there. We want to get even numbers. If we run one, two, three. So if delta x is equal to 3.
Our delta y-- and I'm just doing it because I want to hit an even number here-- our delta y is equal to-- we go down by it's equal to negative 2. So for A, change in y for change in x.
When our change in x is 3, our change in y is negative 2. When we go over by 3, we're going to go down by 2.Image Source: Google Images.
Babies usually follow a straight line of increasing body length as they start growing. This baby was born 20 inches long (y-intercept), and has been growing at .
©l b2e0 E1R2N gKXuVt4a A LSZoTfmtvwxaVrpe j ELGLsC v.o x PA el hl Y UrviNg2hFt Xs9 8r neosWerUv aeZd h.v 7 aM ra cd ieF sw 6i9tNh7 AIln 7fqi0n1iHtbe H 4P urYeU-KAfl Wgwegbfr PaK.w Worksheet by Kuta Software LLC. To write an equation in point-slope form, given a graph of that equation, first determine the slope by picking two points.
Then pick any point on the line and write it . Write and graph the linear equation that gives the distance y in kilometers in terms of the number x in miles. b. What distance in kilometers corresponds to 20 Write an equation in slope -intercept form for.
If the slope of a line is undefined and line goes through the point (-3, ), express the equation of this line in slope-intercept form. Show Answer Since the slope is undefined, the line is a vertical line.
Recall that the slope (m) is the "steepness" of the line and b is the intercept - the point where the line crosses the y-axis. In the figure above, adjust both m and b .