Slope-Intercept Form | Writing an Equation from a Graph | Math with Mr. J

Welcome to Math with Mr. J. In this video, I'm going to cover how to write an equation in slope-intercept form from a graph. And remember, for slope-intercept form, we have y equals mx plus b, with m being the slope and b being the y-intercept. And then x and y are the x and y coordinates of any point on the line. Now, all we need to do here is find the slope and y-intercept. Then we plug those in to our equation for m and b. And we have our equation. The slope and y-intercept give us all the information we need for the equation of a line. So looking at number one, let's start by finding the y-intercept. Then we will find another point on the line and determine what the slope is. And for this example, you can see the two points that we are going to use. They've already been marked. I plotted points there. So for the y-intercept, where does this line cross the y-axis? Well, it looks like this line crosses the y-axis right here at four. So the coordinates are 0, 4. So our y-intercept is 4. Now we find our slope here by going from one point on the line to another point on the line. And we're going to work from left to right here. So we're going to start at that y-intercept and then work our way to that other point. Remember, slope equals rise over run. So we need to determine how far up or down and then how far over we need to go. Well, we need to go up one unit, two units in order to align with the other point. That's our rise. And since we went up, that's a positive 2. So our rise is 2. And then we need to go to the right one unit, two units, three units to get to our other point. So our run is 3, a positive 3 since we went to the right. So rise of 2 over our run of 3. So our slope equals two-thirds. Now we plug two-thirds in for m and four for b. So our equation for this line is y equals two-thirds x plus four. And that's it. We're done. That's our equation. Let's move on to number two. Taking a look at number two here, let's find our slope and y-intercept. Now for number one, our line was going upward as it moved from left to right. It had a positive slope. Now for number two, we can see that the line is moving downward as it moves from left to right. This line has a negative slope. Let's start with the y-intercept and we will go from there. This line crosses the y-axis at 1. So our y-intercept here is 1. Now let's use another point on the line, which I have one marked right here, and we are going to figure out the slope. So we'll work our way from the left point to the right. So let's start with the rise. We need to go down one unit, two units in order to align with the other point. And since we went down, this is going to be a negative 2. Our rise is negative 2. Then we need to go over one unit to the right to get to our other point. So our run is 1 and a positive 1 since we went to the right. So our slope here is rise of negative 2 over our run of 1, which we can write this as just negative 2. So we can simplify that fraction to negative 2. Now all we need to do is write our equation. So we plug in negative 2 for m and 1 for b. So y equals negative 2x plus 1. And we're done. That's our equation for that line. Let's move on to number three. Moving on to number three here, we have a line with a positive slope. It's moving upward as it moves from left to right. Now as far as this example, I don't have the points that we're going to use clearly marked on the line. I don't have the points plotted like I did for numbers 1 and 2. But we're going to do the exact same thing here. We just need to find those points. Our y-intercept is down here at negative 5. So let's use this point. And then we need to find another point on the line that we can easily read, that we can easily use to find the slope. We need to look for something at a grid intersection. We want a point where we can clearly see what the coordinates are. A point where we can clearly find the rise and run. So let's use this point right here. And now let's find our slope. We'll start with the rise. We need to go up one unit, two units, three units, four units, five units, six units. And since we went up, that is a positive. So our rise is six. And then our run, well, we need to go over one unit. And that's to the right. So it's positive. Our run is one. So our slope here, we have a rise of six over a run of one. So six over one, which can be simplified to just six. And then our y-intercept is negative five. Now we can write our equation. So we plug in six for m and negative five for b. So y equals 6x plus negative five. Now, is this equation correct? Yes, it is correct. But we can simplify it here. So we don't have that double sign of addition and a negative. We can rewrite adding a negative as just subtraction. So we can simplify this to y equals 6x minus five. Adding negative five and subtracting five give us the same thing. So either of these equations will work. Now, a lot of times we will see slope-intercept form simplified to show a negative y-intercept as subtraction. So this is something to be aware of. We have this equation right here, where we are adding negative five, or we can simplify that and rewrite it as subtraction. So again, just something to keep in mind when we have negative y-intercepts. Let's move on to number four. Lastly, taking a look at number four here, we have a line with a negative slope. And as far as the y-intercept, that's going to be right here at negative two. Now, we need to look for another point on our line here so we can find the slope. Let's use this point right here. Now, let's find the slope. And we're going to work from the left point to the right point. So starting with the rise, we need to go down one unit, two units, three units, four units, five units. And since we went down, that's negative. So our rise is negative five. And then as far as our run here, we need to go to the right one unit, two units, three units, four units. And since we went to the right, that's positive. So our run is four. Our slope is negative five over four, so negative five-fourths. And then our y-intercept is negative two. So let's write our equation here. Y equals negative five-fourths x plus negative two. Now just like we talked about with number three, we can simplify this. So let's rewrite this using subtraction. So we can simplify this equation and rewrite it as negative five-fourths x minus two. So here's our equation with adding negative two. Or we can simplify that and rewrite it with subtraction. So there you have it. There's how to write an equation in slope-intercept form from a graph. I hope that helped. Thanks so much for watching. Until next time, peace.