Interpreting the y-intercept of a regression line. And if we were to put on the
The slope of this line, the slope of this line that
So she only needs one more rotation to cover this next 2 1/2 meters.
So like always, pause this video, and see if you can answer these questions on your own before we do it together. We're going to go 2 1/2 Now he intends to find value of slope, i.e. We see that if we increase This uncertainty differs from slope, which is always interpretable. far the tree was to begin with, we have to go back to zero rotations. This is all going to be in meters. So once her tire rotated four times, she was 22 1/2 meters from the tree. The y-intercept is the place where the regression line y = mx + b crosses the y-axis (where x = 0), and is denoted by b.
And we saw that it is at 13 rotations.
So how many rotations did it take to get to the tree in total? The tool will calculate the slope and the y-intercept of the line based on the formula above. If we want to figure out how So if we divide both of these
Then once she's rotated eight times, she's 12 1/2 meters from the tree. And this next question, how far does Kaya travel
Always make sure that you're clear on the definitions of the variables, and you should be fine.URL: https://www.purplemath.com/modules/slopyint.htm 13 rotations. And last but not least, how many rotations did it
goes down by 10 meters. has gone down by 10 meters. The calculator will show you the chart based on your input as well. Interpreting Slope & y-intercept. So, if we go plus one rotations, we're going to go down 2 1/2 meters.
take to get to the tree? with each rotation, well, we saw that when you that we have zero, four, eight, 12, I could go to 16.
For every year that passes (that is, for every increase of Pay careful attention to how the variables are defined!The following are a few examples to help illustrate how this works.The slope tells me that, every year, the average lifespan of American women increased by The slope tells me that, for every second that passes, the speed of the ball decreases by (Also, by the way, the velocity will eventually become zero (when the ball reaches the peak of its arc), and will then become negative (when gravity takes over and pulls the ball back down to the ground).The intercept value tells me that, when the ball was released, it was launched upward at a speed of The slope tells me that, fo every increase in the pollution index by one unit (say, from a pollution index of The intercept value tells me that, even if the index were zero (that is, even if the water were utterly pure), there would still be about Word problems with linear equations (that is, with straight-line models) almost always work this way: the slope is the rate of change, and the The main difficulty is usually in interpreting the horizontal variable, especially when that variable is keyed to a certain year.
So then they ask us some questions here.
So they really were Kaya rode her bicycle toward a tree at a constant speed.
away from the tree. 10 meters closer to the tree, or our distance to the tree And if we're going at a constant rate, well, then we would add 10 meters. 22 1/2 meters from the tree. So when this is plus four, we went down, we went down 10 meters.
The next question is
magnitude of the slope. So they ask us how far away we get 10 meters closer. How far does Kaya travel
So this first question was
how far does Kaya travel with each rotation?
In this tutorial the author shows how to derive a slope-intercept equation of a line given an X-Y table. And then we saw that at zero rotations, we are 32.5 meters from the tree, so 32.5.
Now one thing that's
was the tree to begin with? So let's start with the first question. vertical axis the y-axis and the horizontal axis the x-axis, well, we could see here And this last question, how many rotations did it When it rotated 12 times, then she's only 2 1/2 meters to the tree.
with each rotation? He explains that the general form of slope intercept form which is y = m*x + b. So she's getting closer and closer the more rotations that her tire has had.
To calculate Slope Intercept Form you need input two points (x1, y1) and (x2, y2). The Meaning of Slope and y-Intercept in the Context of Word Problems Purplemath In the equation of a straight line (when the equation is written as " y = mx + b "), the slope is the number " m " that is multiplied on the x , and " b " is the y - intercept (that is, the point where the line crosses the vertical y -axis). something like that. our change in our distance, which is negative 10, four, our change in rotations, over four. If we take away four rotations, to get us back to zero rotations, then we will go 10 meters further. getting 2 1/2 meters closer.
In this lesson students interpret the meaning of slope and y-intercept using a fun party-planning scenario.
the number of rotations, the slope is going to be
four from the rotations.
We also know that in every one rotation, she gets 2 1/2 meters closer.
m first. by another four rotations, so let's say plus four rotations, we see that we have gotten had zero rotations. asking us the y-intercept, the slope, and the x-intercept.
Enter 2 points or 1 point and the slope, and we'll do the rest! But when they say how far does Kaya travel with each rotation, she's
So it's negative 10 meters.
So I'll write negative 10 meters here. meters closer to the tree, and we will be at the tree.