Find the slope of the line through each pair of points (-(4)/(3), (1)/(2)) and ((1)/(3),-(5)/(6

step 1 Hey everyone. All right. So they give us two points. They give us the point negative four thirds

Find the slope of the line through each pair of points...

Key Concepts

Difference Quotient (Slope Formula)

The slope is computed using the difference quotient formula, which is given by m = (y? - y?) / (x? - x?), where (x?, y?) and (x?, y?) are two distinct points on the line. This formula captures the idea of the rate of change between the two points, making it essential for understanding linear relationships in algebra.

Slope of a Line

The slope of a line measures its steepness and direction, defined as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run) between any two distinct points on the line. It is a fundamental concept in coordinate geometry that describes how much the y-coordinate changes for a given change in the x-coordinate.

Transcript

0:00 Hey everyone.

00:01 All right.

00:02 So they give us two points.

00:03 They give us the point negative four thirds and the point or y value one half.

00:12 And they give us the point one third with the y value negative.

00:20 All right.

00:21 And they want us to find these slope.

00:23 So we know slope, which is m, is your change of y over a change of x.

00:29 Now, to be able to find your change of y over change of x, you can use a formula.

00:34 Y2 minus y1 divided by x2 minus x1.

00:43 Now, before we can really get into plugging in, we really need to make sure that we know what's our first point and what's the second point.

00:50 I'm going to go on label.

00:51 I'm going to take this as my first point and the second as my.

00:55 Okay.

00:56 Now that i have this label, it's a little bit easier for me to see, i can start plugging in.

01:01 So i'm going to take the y value of my second point.

01:03 Y value of my second point, which is 5 over 6, and i'm going to subtract the y value of my first point, which is one half.

01:14 And i'm going to divide that by the x value of my second point, which is one -third, minus the x value of my first point.

01:25 Now, since it's a negative, i'm just going to put it in parentheses.

01:30 All right, so now we're going to go when we want to subtract.

01:33 But if we look at this denominator up top so are they the same no so we can't subtract it we gotta get them the same so we have to find our least common denominator now your least common denominator between six and two is going to be so we're gonna have six as our denominators now to get from six to six did we have to do anything no so we're gonna leave this minus five we have our subtraction sign in the middle and then to get from two to six i have to multiply by three so i also have to do that up top.

02:08 So i'll take this 1 and multiply it by 3 to get my new number, which is 3...

Please give Ace some feedback