Find an expression for the function whose graph is the given curve. The line segment joining the

step 1 Today, we are given two points. The two points are negative 5, 10, and 7 negative 10. And we are

Find an expression for the function whose graph is the given...

Key Concepts

Domain Restriction

When a function is defined only over a particular segment of a line, its domain is limited to the x-values corresponding to that segment. This emphasizes that the function is only applicable within a certain interval, rather than for all values.

Linear Function

A linear function is one whose graph is a straight line, characterized by a constant slope and represented generally by the form y = mx + b, where m is the slope and b is the y-intercept.

Slope of a Line

This concept involves calculating the rate of change of a line by taking the difference in the y-values divided by the difference in the x-values between any two points. It is fundamental when determining the direction and steepness of a line.

Point-Slope Form

This is a method of expressing the equation of a line using the slope and the coordinates of one point on the line. It is written in the form y - y? = m(x - x?), where m is the slope and (x?, y?) is a specific point on the line.

Transcript

00:01 Today, we are given two points.

00:03 The two points are negative 5, 10, and 7 negative 10.

00:12 And we are supposed to find the equation that essentially lies on these two points.

00:17 We can draw a picture to essentially illustrate the location of these two points.

00:24 So our first point, negative 510, lies in the second quadrant here.

00:30 Again, this is just general.

00:32 This is not exact.

00:34 And our second point 7 negative 10 lies in the fourth quadrant.

00:43 In order to find the equation of these two points, first we need to find the slope.

00:50 Now, our slope is equal to the change in y over the change in x.

00:56 Or in other words, more specifically, y2 minus y1 over x2 minus x1.

01:03 A lot of students always ask, how do i know which y, which point is our first point and which one is our second point? well, our leftmost point, which in this case is going to be negative 510, is going to be our y1 and our x1, and the rightmost point is going to be our y2 and our x2.

01:25 So the left most point is always going to be the first set of points, and the right most point is going to be the second set of points.

01:34 Now we can label these, y2, x2.

01:40 Y1, x1.

01:41 Now that we haven't labeled, we can start plugging in our answers.

01:45 So y2 is negative 10.

01:47 Y1 is going to be 10.

01:50 X2, in our case, is 7.

01:54 And x1 is going to be negative 5.

01:57 We all know that a negative and a negative equals a positive.

02:01 Our answer becomes negative 20 over 12.

02:05 We can still simplify by dividing the top and the bottom by 4.

02:11 And our simplified slope is going to be negative 5 over 3.