How to Find the Slope and Y-Intercept from Slope Intercept Form | Math with Mr. J

Welcome to Math with Mr. J. In this video, I'm going to cover how to find the slope and y intercept from slope intercept form. Now, remember slope intercept form is a way to write the equation of a line. So, we can write and graph equations of lines using this form. Slope intercept form is right here. We have y = mx + b. Although this may look confusing at first, once we understand what the letters we are looking at represent, this will become much more clear. We're going to start by focusing on two of the letters m and b. m is going to be the slope of the line. Remember, slope tells us how steep a line is. So how much a line changes vertically up and down as it moves horizontally side to side. Then B is going to be the y intercept. The y intercept is where the line crosses the y ais. So m is the slope and b is the y intercept. And that's why we call this slope intercept form. This gives us all the information we need to graph a line. And then the x and y are variables representing the x and y coordinates of any point on the line. So when writing in slope intercept form, we can leave those as just x and y. Let's jump into number one where we have y = 4x + 6. So what's our slope and y intercept here? Well, our slope is next to the x, so four. And then as far as the y intercept, we have + 6 here. So the y intercept is six, a positive six. And that's our slope and y intercept. Let's move on to number two where we have -35s x - 10. Our slope is -35ths. And then for our y intercept, we don't have plus b here. We don't have plus our y intercept. Well, we're actually working with a negative y intercept here. So we have subtraction. Our y intercept is 10. Now this equation has been simplified. So we don't have plus a -10 here. Meaning this can be written as y = -35s x + 10. And that does make that -10 a little more clear. But equations will a lot of times be simplified to showing that as just subtraction. So we don't have that double sign of addition and then the negative. Subtracting 10 gives us the same thing as adding -10. So either of these equations will work here. Just something to be aware of when working with negatives. Let's move on to number three where we have y = 2x. Our slope here is going to be 2. But what about the y intercept? We only have 2x here. Well, let me rewrite this as y = 2x + 0. Our y intercept is zero here. Adding zero doesn't change the value of anything here. It's not changing the value of that side of the equation. So this can just be written as y = 2x. So whenever you see something like this, the y intercept is zero. We have + 0. And feel free to rewrite the equation with plus 0 to make that y intercept clear. Moving on to number four, we have y = x - 3. Now for our slope here we just have an x. Remember whenever we just have an x there is an implied 1 in front. So our slope is one. Here we can think of this as y = 1x - 3 and then our y intercept is3. Now for this equation it can be helpful to rewrite this as y equ= 1 x. So writing in that one plus -3. So again we can write that one in front of the x and then add -3 in order to make our slope and y intercept a little more clear for us here. Either equation will work though. So use what works best for you. Moving on to number five, we have y = -x + 1/4. So going off of number four, we can think of this as y = -1x + 1/4. So our slope is -1 and then the y intercept is 1/4. Lastly, let's move on to number six where we have y = 7. Let me rewrite this one to make the slope and y intercept a little easier to find. So, we can also write this one as y equ= 0x + 7 and that's a positive 7. So, plus 7. Now we can see that our slope is zero and our y intercept is seven. So slope of zero and y intercept of 7. Since we have 0x which is just zero, we can write our slope intercept form without it and write this as just y = 7. Remember a slope of zero means we have a horizontal line. So this is just a horizontal line that goes through seven on the y ais. So there you have it. There's how to identify the slope and y intercept from slope intercept form. I hope that helped. Thanks so much for watching. Until next time, peace.