Sketch by hand the line that passes through the points (1,-2) and (3,2).

Name: Problem 77, Chapter 2: A Graphical Approach to Precalculus with Limits
Uploaded: 2020-08-17T15:29:59-08:00
Duration: 3 min 26 s
Channel: Nick Johnson
Description: Sketch by hand the line that passes through the points (1,-2) and (3,2).

step 1 We want to sketch a line that passes through these two points. So 1, negative 2 and 3 .2. Well,

Sketch by hand the line that passes through the points...

Key Concepts

Slope

The slope is a measure of a line's steepness and direction, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It is fundamental in understanding how rapidly one variable changes in relation to another.

Point-Slope Form

The point-slope form is a method for writing the equation of a line, which uses the slope and the coordinates of a point on the line. This form, expressed as y - y? = m(x - x?), provides a straightforward way to derive the line's equation from two known points.

Graphing Linear Equations

Graphing a linear equation involves plotting points on a coordinate plane that satisfy the equation and drawing the line that passes through them. This process not only visualizes the solution set of the equation but also helps in understanding the relationship between the variables.

Coordinate Plane

The coordinate plane, consisting of a horizontal x-axis and a vertical y-axis, serves as the framework for graphing equations. It allows for the representation of algebraic relationships and geometric figures in a two-dimensional space.

Transcript

00:01 We want to sketch a line that passes through these two points.

00:03 So 1, negative 2 and 3 .2.

00:05 Well, if we can find a slope, we could easily grab this line.

00:10 Let's find a slope, or we have two points.

00:13 The slope is just, well, change in y over change in x.

00:18 So you can call either one of these points, 0 .1 and point 2, and then slope is just, well, y2 minus y1, divided by x.

00:30 2 minus x1 right just the change in your y over your change in your x so let's just take well let's call this point 1 .2 so the slope here is going to be well so we have 2 minus a minus 2 right if this is y2 and this is y 1 we have 2 minus a minus 2 minus 2 with 2 plus 2 we have 2 plus 2 over 3 minus 1 or 2 plus 2 that is 4 over 3 minus 1 is 2 so 4 over 2 is 2 is equal 2.

01:00 To two.

01:01 So therefore our slope is two, which is two over one.

01:05 So slope, right, is rise over one.

01:07 Run.

01:08 So pick either of these points you want.

01:14 And then, well, actually, we really didn't, i mean, do we need to find? is i discussed by hand the line that passes through these two points? okay.

01:27 So, whoops.

01:28 So we know that, right, both of these points are on the line, and the slope or line is two.

01:35 So go ahead.

01:37 We draw our axes here, x, y, axes.

01:43 So we know what, we have a point.

01:45 Well, we have a point three, two.

01:47 So three two is on the graph...