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Solving Linear Equations by Graphing: Time-Distance Relationships

8.EE.A.1

auto-gen

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

8.EE.A.2

Squares and square roots

Square Root of a Perfect Square

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

8.EE.A.3

Scientific notation

8.EE.B.5

Parallel and perpendicular lines in linear functions

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Identifying proportional relationships

8.EE.B.6

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

8.EE.C.7

Introduction to linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Two-step Linear Equations RHS

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

8.EE.C.8

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

8.F.A.1

Relationship between two variables

Identifying functions

8.F.A.2

Function notation

8.F.B.4

Applications of linear relations

8.F.B.5

Graphing linear functions using table of values

8.G.A.1

Line symmetry

Tessellations using translations and reflections

tessellations using translations and reflections

8.G.A.2

Rotational symmetry and transformations

8.G.A.3

Enlargements and reductions with scale factors

Tessellations using rotations

8.G.A.4

Similar polygons

8.G.A.5

Similar triangles

8.G.B.6

Pythagorean theorem

Pythagorean Theorem

8.G.B.7

Using the pythagorean relationship

8.G.B.8

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Applications of pythagorean theorem

8.G.C.9

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of cones

Surface area and volume of spheres

8.NS.A.1

Understanding the number systems

Rational vs. Irrational numbers

8.NS.A.2

Determine square roots of rational numbers

Square roots of rational numbers

Estimating square roots

Converting repeating decimals to fractions

8.SP.A.1

Reading linear relation graphs

Box-and-whisker plots and scatter plots

8.SP.A.2

Solving linear equations by graphing

8th Grade Math

math

Intro

Ex. 1:

Ex. 2:

Ex. 3:

Ex. 4:

- Hi, welcome to this question right here. So we&apos;ve got a graph here set up for us already, trying to show us the relationship between the temperature in degree Celsius versus the time underneath right here which is in minute, okay? It looks like a very straight single straight lines. So guess what, if you see a straight line it means you're looking at a y equals mx plus b graph, okay? 
Now remember, the y is your y-axis. So in this case I'm going to put down the degree Celsius right here in the position of the y. The m, if you don't remember what m is, it's the slope of the graph, okay? So we're going to figure out the slope later. The x, so we draw a box with a slope and the x is the x axis. So it's in the time and we just use the variable t, but just remember as in terms of a minute for this question. Now the b is known as the y-intercept on the graph. The y-intercept is where the graph would touch the y-axis. If I just kind of look at the graph right here. If it is just going straight down like this, it will probably enter the zero go across the zero. So in this question here, you don't have a b for your equation, okay? Just leave it out, but the problem is how do you figure out the slope? Well remember, you might want to learn it right now, the slope is equal to the rise over run, okay? It's basically how the graphs behaves, going up first and turn left or right. Now, this is how we do it. You can pick two points. Let's say I pick these two points right here. Now just ask yourself, 
"How can I go from here to here?" Well, if I'm just using the rise over run which is the slope, which is the m over here, okay? 
All we had to do is just think about that in order for me to go from here to here, I need to go up 20 units first, okay? So this is 20, this is 40, so the difference is that I need to go up 20. So the rise in this case will be 20 and it's positive. Why, because you're going up. If you're going down, it'll be negative. Okay? Then in order for me to go from this point to here, I need to travel from two minutes to four minutes. That's a difference of two minutes. So that means I need to go to my right side two minutes. So it's positive because you're going toward the right. If you're going towards the left, it's negative. Okay? So 20 over two, what do you get? You don't need a calculator for that, at least for me I don't need one. Ten, okay so the 10 is actually your slope which is represented by the m in the equation. So guess what, it goes in here, 10t okay? 
So the relationship between the degree Celsius right here versus the time is just that the degree, the temperature is equal to 10 times the t, that's it. So the equation here, the equation for that relationship is right over here. You can either use this one right here or feel free to go y equals to 10 times the x. You can also use this equation, okay? Oh, where did it go? 
Y equals to 10 times the x, okay? So that way, it's easier. All right, but if you want to use the variables from the question, then it will be the degree Celsius equals the 10 times the t. All right? Let's check on the next--

We will learn how to plot linear equations, and then use the graphs as an aid to answer questions about the linear relations. Alternatively, we can find out the linear equations from their graphs. In addition, we will learn how to plot graphs and determine their equations when we are given the table of values of linear relations. We will also explore the concepts of interpolating and extrapolating data from graphs of linear equations.  

Solving linear systems by graphing

Solving systems of linear equations with graphing