Find the slope and -intercept and use them to draw the graph of the line. 5 y-8 x=30

Name: Problem 43, Chapter 2: Intermediate Algebra
Uploaded: 2020-08-03T14:10:07-08:00
Duration: 4 min 25 s
Channel: Erin Kearney
Description: Find the slope and -intercept and use them to draw the graph of the line. 5 y-8 x=30

Find the slope and -intercept and use them to draw the graph...

Key Concepts

Graphing a Line

Graphing a line involves plotting the y-intercept on the coordinate plane and then using the slope to find another point on the line. Once two points are determined, they can be connected with a straight line, providing a visual representation of the linear equation.

Y-intercept

The y-intercept is the point at which a line crosses the y-axis, corresponding to the value of y when x is zero. This point is significant because it serves as an initial value from which the rest of the line can be graphed using the slope.

Slope

The slope is a measure of the steepness and direction of a line. It is calculated as the ratio of the change in y (vertical change) to the change in x (horizontal change) between any two points on the line. It determines whether the line rises, falls, or remains horizontal as it moves from left to right.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope and b represents the y-intercept. This form is useful as it immediately reveals the important attributes of the line, aiding in graph interpretation and analysis.

Transcript

00:01 So my goal here is to find the slope and the y intercept of my equation and then use that information to graph the line.

00:08 Now remember, slope is the variable m, y intercept is the variable b, which brings to mind the equation y equals mx plus b.

00:18 So that means i need to have this equation written in slope intercept form, which is y equals mx plus b.

00:24 And the kind of standout is that y is isolated, which here it is not.

00:28 So that's going to be my first task is to get this equation into slope interception.

00:31 Intercept form, then i can identify my slope in my y intercept, and then i can wrap.

00:36 So to get y by itself, y is being multiplied by 5, it's also being subtracted by 8x.

00:42 So since when i solve, i go in reverse pemdas, i get rid of, i'm going to get rid of my subtraction before my multiplication.

00:48 So i'm going to get rid of minus 8x by adding 8x, which would make, bring my equal sign straight down, that would now have 5y by itself.

01:00 And on the right hand side, oops, that should have an x attached to it, on the right hand side, on right hand side, 30 and 8x are not like terms, so i can't actually add them together.

01:09 I can just show that i want to add them.

01:12 So 30 plus 8x.

01:14 Now to get rid of the 5, i'm going to divide by 5.

01:18 Now when i do that on the right, i want to make one big fraction because i want to make sure that i'm dividing both 30 and 8x by 5.

01:25 So again, i'll bring my y straight down.

01:27 It's by itself.

01:29 And so then i use this little trick to help myself visualize what i'm dividing, which is going like this.

01:37 I call it the beans because it kind of looks like a bean.

01:40 So 30 divided by 5, that would be 6.

01:44 I bring down my plus sign because that's what i have.

01:47 And then i've got 8x divided by 5.

01:52 Now i see a fraction here.