Algebra Tutorials!
Sunday 16th of June
Calculations with Negative Numbers
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
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Graphing Using x- and y- Intercepts

Once we know both the x-intercept and the y-intercept, we can graph the equation.


Example 1

Graph 3x + 5y = 15 using the x- and y- intercept.


First, find the intercepts.

To find the y -intercept, let x = 0. To find the x-intercept, let y = 0.
3 · 0 + 5y = 15 3x + 5 · 0 = 15
5y = 15 3x = 15
y = 3 x = 5
The y-intercept is 3. The x-intercept is 5.
The ordered pair is (0, 3). The ordered pair is ( 5, 0)

We now graph these two points and draw the line that contains them.


Slope-Intercept Form

The slope-intercept form is a special case of the point-slope form, where the given point of the line (x 0 , y 0 ) lies on the y-axis, so x 0 = 0. This means that the equation is of the form y - y 0 = mx, or y = mx + y 0 . So, the equation is given explicitly when we know both the intercept and the slope and it is simpler than the more general point-slope form. This is the most common form for the equation of a line.

Key Idea An equation for a line is said to be in slope-intercept form when it is of the form y = mx + b, where m is the slope of the line and b is the y-coordinate of the y-intercept. Any line that is not vertical has an equation that can be written in slope-intercept form.

The equation of a vertical line cannot be written in slope-intercept form because the slope of a vertical line is undefined; that is, it has no slope.

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