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Graph linear functions using a slope and point

Analyze puzzles and games that involve numerical reasoning using problem-solving strategies

Arithmetic sequences

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Arithmetic series

Arithmetic series formula

Geometric sequences

Arithmetic mean vs. Geometric mean

Model and draw 3-D objects and their views

Surface area of 3-dimensional shapes

Characteristics of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Applications of quadratic functions

Draw and describe exploded views component parts and scale diagrams of simple 3-D objects

Similar triangles

Similar polygons

Converting from general to vertex form by completing the square

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Completing the square

Completing the Square

Solve problems that involve personal budgets

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Applications of rational equations

Applications of inequalities

Demonstrate understanding of financial institution services used to access and manage finances

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Demonstrate understanding of slope as rise over run and rate of change by solving problems

Direct variation

Identifying direct variations

Inverse variation

Joint and combined variation

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>

Rate of change

Solve problems by applying proportional reasoning and unit analysis

Solving rational equations

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Solve problems that require manipulation and application of formulas related to slope and rate of change

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Transformations of quadratic functions

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Quadratic function in vertex form: y = a(x-p)^2 + q

Solve problems that involve scale

Enlargements and reductions with scale factors

Scale diagrams

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Simplifying complex fractions

Demonstrate understanding of linear relations by recognizing patterns trends graphing creating tables

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Applications of linear relations

System of linear equations

System of linear-quadratic equations

Graphing linear inequalities in two variables

Graphing systems of linear inequalities

Solve problems that involve two and three right triangles

Unit circle

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Grade 11 Essential Mathematics (30S) - Half Course 4

Develop critical thinking skills

Develop spatial sense

Develop an understanding of managing money

Develop proportional reasoning

Develop spatial sense related to triangles

math

Ex. 1

Ex. 2

- Hi, welcome to this question right here. So, we're given the point and the slope and we need to draw the graph. Now, this is actually very, very easy. See, what happens is, we don't even need to show any work. Let's say the graph in a standard precision. You do know you have a point, and that point is at negative 3, so you go left 3 and up 2. So you're at somewhere over here, correct? If you have a grid paper, obviously you can do a much better job that I am. So, you know this slope is 2 over 3, so that means you're going from this point, you're gonna go up 2 and over 3 this way. So, let's say just go up 2 right there and you go over 3, so you should be hitting on this point right there. That's 2 points up from here so, if I just kind of draw the little bit of curly direction right here and go over 3. Once you have two points, using the gridded ruler or anything that is straight, and you just simply draw like a straight line connecting the two points and therefore, that's your graph, OK? And that's the final answer. Thanks for watching.

Graphing a line from point (-3, 2) with slope 2/3

Plotting a line from a point using a negative slope of -3/5

Graphing a line through a point with undefined slope

Graphing a horizontal line through a point with slope 0

Graphing a line from the x-intercept with a negative slope

Graphing a line from y-intercept and slope 3/2

Finding x-intercept, y-intercept, and slope from a graph

Finding intercepts and slope from a graph using rise over run

Identifying intercepts and slope of a vertical line

Identifying intercepts and slope of a horizontal line

If we are given a single point and the slope of a straight line, we will be able to graph it. By the same token, we can determine the slope and intercepts if we are given from its graph.

Graph using a single point and slope

Graphing linear functions using a single point and gradient

Solving linear equations by graphing

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using a single point and slope

What You'll Learn

Plot a point on the coordinate plane using given coordinates

Apply slope as rise over run to find a second point from the first

Draw a linear function by connecting two points with a straight line

Identify x-intercepts and y-intercepts from a graph of a line

Calculate slope from a graph using two known points

Recognize special cases: zero slope for horizontal lines and undefined slope for vertical lines

What You'll Practice

Graphing lines given a point and positive or negative slope

Plotting lines with slope in fraction form using rise over run

Drawing horizontal and vertical lines with zero and undefined slopes

Finding x-intercepts, y-intercepts, and slope from given graphs

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

10 Video lessons

Skills

Graphing

Slope

Intercepts

Linear Functions

Coordinate Plane

Rise Over Run

Point-Slope Method