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Finding the Greatest Common Factor
Factoring Trinomials
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Solving Equations with One Radical Term
Adding Fractions
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The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
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Multiplying and Dividing in Scientific Notation
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Multiplication by 111
Adding Fractions
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Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
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Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
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Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
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Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
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Writing Linear Equations in Slope-Intercept Form

Objective Learn the slope-intercept form of the equation defining a line.

The slope-intercept form is an extremely useful special case of the point-slope form of the equation defining a straight line. It is written as y = mx + b, where m is the slope and b is the y-intercept, the point where the line intersects the y-axis. The x- and y-intercepts of a line are the points where the line intersects the x- and y-axes, respectively.

First, we will try to answer the question “How can we determine the x- and y-intercepts of a line that is given in the form of an equation?”

Then we will learn how to find the intercepts algebraically by solving linear equations. This can be done whether the equations are in standard form or in point-slope form.


Example 1

Find the y-intercept of the graph of 2x + 3y = 12.


This equation is in standard form. The y-intercept is the intersection of the line and the y-axis, so it is a point that is both on the line and on the y-axis. It satisfies the following equations.

2x + 3y = 12 Equation of the line
x = 0 Equation of the y-axis

To find the y-intercept, let x = 0 in the equation of the line.

2x + 3y = 12  
2(0) + 3y = 12 Let x = 0.
3y = 12  
y = 4 Divide each side by 3.

The y-intercept of this line is 4, so the line crosses the y-axis at (0, 4).


Example 2

Find the y-intercept of the graph of 2( y - 1) = 5( x + 2).


This equation is in point-slope form. As in the case of standard form, let x = 0 and solve for y.

2( y - 1) = 5( x + 2)  
2( y - 1) = 5( 0 + 2) Let x = 0.
2y - 2 = 10 Distributive Property
2y = 12 Add 2 to each side.
y = 6 Divide each side by 2.

So, the y-intercept is 6 and the line crosses the y-axis at (0, 6).

To find the x-intercept, let y = 0 in the equation, since the x-axis is given by the equation y = 0. Practice finding the x and y-intercepts of the graphs of equations.

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