2. Modeling with Linear Functions, Linear Systems, & Exponential Functions

2.01 Graphing systems of equations

2.02 Solving systems of equations with the substitution method

2.03 Solving systems of equations with the elimination method

2.04 Solving systems of equations with a variety of methods

2.05 Applications of linear systems

2.06 Graphing linear inequalities in two variables

2.07 Systems of inequalities

2.08 Functions and relations

2.09 Domain and range and set notation

2.10 Evaluating functions

2.11 Modeling linear relationships

2.12 Review: Laws of exponents

2.13 Exponential growth and decay

Investigation: Comparisons of simple and compound interest

2.15 Compound interest

2.16 The slope formula

2.17 Transformations of y=x

Investigation: Exploring slopes and equations of lines

Investigation: Relationship between shoulder span and height

2.18 Slope-intercept form

2.19 Standard form

2.20 Point-slope form

2.21 Comparing linear relationships

2.22 Comparing exponential relationships

2.23 Comparing linear and exponential relationships

2.24 Review: Slope as rate of change

2.25 Key features of quadratic functions

2.26 Graphing quadratic functions

2.27 Quadratic functions and technology

2.28 Extension: Absolute value equations

2.29 Extension: Absolute value inequalities

2.30 Graphs and characteristics of absolute value functions

United States of America NJ

Algebra 1

2.20 Point-slope form

Interactive practice questions

For each of the following equations, determine which form they are written in.

a

$y=-4x+5$y=−4x+5

Standard form

A

Slope-intercept form

B

Point-slope form

C

b

$y-1=5\left(x-4\right)$y−1=5(x−4)

Standard form

A

Slope-intercept form

B

Point-slope form

C

c

$5x-3y=8$5x−3y=8

Standard form

A

Slope-intercept form

B

Point-slope form

C

Easy

< 1min

Write the point-slope form of the equation of a non-vertical line with slope $m$m that passes through the point $\left(x_1,y_1\right)$(x1,y1).

Easy

1min

Which of the following is true of a straight line with slope $1$1 going through point $A$A($2$2, $4$4)?

Easy

< 1min

Which of the following equations is in point-slope form?

Easy

< 1min

Outcomes

F.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.C.7.A

Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.C.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.LE.A.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

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