It is therefore a straight horizontal line through 5 on the y axis. Play with different values of b and observe the result. The value of m is 0. This is a simple linear equation and so is a straight line whose slope is 0. That is, y increases by 0. Have questions on basic mathematical concepts? Become a problem-solving champ using logic, not rules. Learn the why behind math with our certified experts.
How to Find the Slope of a Line? What Does the Slope of a Line Mean? Explore math program. Explore coding program. Make your child naturally math minded.
Most questions answered within 4 hours. Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. So our line is going to look- you only need two points to define a line, our line is going to like, let me do this in this color right over here. Our line is going to look like, is going to look, is going to look something like, is going to look, let me see if I can, I didn't draw it completely at scale, but it's going to look something like this.
This is the line, this is the line, y is equal to 2x plus three. But we already figured out that its slope is equal to two, when our change in x is one, when our change in x is one, our change in y is two.
If our change in x was negative one, if our change in x was negative one, our change in y is negative two. And you can see that, if from zero we went, we went down one, if we went to negative one, then what's our y going to be? Two times negative one is negative two plus three is one. So we see that, the point negative one comma one is on the line as well. So the slope here, our change in y over change in x, if we're going from between any two points on this line, is always going to be two.
But where do you see two in this original equation? Well you see the two right over here. And when you write something in slop-intercept form, where you explicitly solve for y, y is equal to some constant times x to the first power plus some other constant, the second one is going to be your intercept, your y-intercept, or it's going to be a way to figure out the y-intercept, the intercept itself is this point, the point at which the line intercepts the y axis, and then this two is going to represent your slope.
And that makes sense because every time you increase x by one, you're gonna multiply that by two, so you're gonna increase y by two. So this is just a, kinda of a get your feet wet with the idea of slope-intercept form, but you'll see, at least for me, this is the easiest form for me to think about what the graph of something looks like, because if you were given another, if you were given another linear equation, let's say y is equal to negative x, negative x plus two.
Well immediately you say, okay look, my yintercept is going to be the point zero comma two, so I'm gonna intersect the y axis right at that point, and then I have a slope of, the coefficient here is really just negative one, so I have a slope of negative one.
So as we increase x by one, we're gonna decrease y by one. Increase x by one, you're gonna decrease y by one. If you increase x by two, you're gonna decrease y by two. And so our line is gonna look something like this. Let me see if I can draw it relatively neatly. It's going to look something, I think I can do a little bit better than that. It's 'cus my graph paper is hand drawn. It's not ideal, but I think you get, you get the point.
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