Find the slope of the line containing the points ( − 1 , 1 ) \left(-1,1\right) and ( 4 , 3 ) \left(4,3\right) .

Hey, everyone. Welcome back. So in this problem, we're gonna find the slope of a line. So we're gonna calculate the slope of a line containing the two points negative 1 comma 1 and 4 comma 3. So remember the slope is the steepness of a line. It's the rise over the run, but notice that we're not given a graph here. And so instead, we're gonna have to use we're gonna have to use the sort of more mathematical definition of the slope, which includes the y twos and y ones, x twos, x ones, stuff like that. So if you don't have the graph, this is gonna be way easier to plug these points into an equation to go ahead and solve for the slope. So you can pick any 2 points, any of these 2 to be your x one y one. It actually doesn't matter. The order of points doesn't matter here. However, what happens is this is the more left this is the leftmost point because notice how the x coordinate is negative one, whereas this x coordinate is 4. So this is gonna be the good x one y one to use in this case. So this is my x one y one, and this is my x two y two. So now we're just going to use this equation over here. We're just going to use m equals y2 minuteus y1 over x2 minuteus x1, and just gonna plug out and plug in some numbers. So my y2, in this case, is 3, my x my y1, in this case, is 1, and then my x 2 is 4, and my x one is negative one. However, what happens here is I have to subtract now a negative number, so it's really important that you stick in the appropriate amount of minus signs there. You don't drop 1. Otherwise, you're gonna get the wrong answer. So just be aware of the minus signs. And now we're just gonna go ahead and calculate this. 3 minus 1 is 2 on the top, and then 4 minus a minus one actually ends up being 4+1. So this slope actually ends up being 2 5ths. It's 2 over 5. So if you were to plot this line over here, it would look like this, in which the distance between any two points, the rise over the run, would basically be a delta y of 2 and a delta x of 5. So you have to go up 2 and over 5, and the slope of the line would end up being probably looking something like this. Alright? That's how to calculate the slope when you're just given 2 points and not a graph. Let me know if you have any questions. Thanks for watching.

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Multiple Choice

Find the slope of the line containing the points $open paren negative 1 comma 1 close paren$ and $open paren 4 comma 3 close paren$ .

$m = \frac{5}{2}$

$m = \frac{2}{5}$

$m equals 2$

$m = \frac{4}{3}$

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Find the slope of the line containing the points $open paren negative 1 comma 1 close paren$ and $open paren 4 comma 3 close paren$ .