FreeAlgebra Tutorials!   Home Elimination Using Multiplication Prime Factors Equations Involving Rational Exponents Working with Percentages and Proportions Rational Expressions Interval Notation and Graphs Simplifying Complex Fractions Dividing Whole Numbers with Long Division Solving Compound Linear Inequalities Raising a Quotient to a Power Solving Rational Equations Solving Inequalities Adding with Negative Numbers Quadratic Inequalities Dividing Monomials Using the Discriminant in Factoring Solving Equations by Factoring Subtracting Polynomials Cube Root The Quadratic Formula Multiply by the Reciprocal Relating Equations and Graphs for Quadratic Functions Multiplying a Polynomial by a Monomial Calculating Percentages Solving Systems of Equations using Substitution Comparing Fractions Solving Equations Containing Rational Expressions Factoring Polynomials Negative Rational Exponents Roots and Radicals Intercepts Given Ordered Pairs and Lines Factoring Polynomials Solving Linear Inequalities Powers Mixed Expressions and Complex Fractions Solving Equations by Multiplying or Dividing The Addition Method Finding the Equation of an Inverse Function Solving Compound Linear Inequalities Multiplying and Dividing With Square Roots Exponents and Their Properties Equations as Functions http: Factoring Trinomials Solving Quadratic Equations by Completing the Square Dividing by Decimals Lines and Equations Simplifying Complex Fractions Graphing Solution Sets for Inequalities Standard Form for the Equation of a Line Fractions Checking Division with Multiplication Elimination Using Addition and Subtraction Complex Fractions Multiplication Property of Equality Solving Proportions Using Cross Multiplication Product and Quotient of Functions Adding Quadratic Functions Conjugates Factoring Solving Compound Inequalities Operating with Complex Numbers Equivalent Fractions Changing Improper Fractions to Mixed Numbers Multiplying by a Monomial Solving Linear Equations and Inequalities Graphically Dividing Polynomials by Monomials Multiplying Cube Roots Operations with Monomials Properties of Exponents Percents Arithmetics Mixed Numbers and Improper Fractions Equations Quadratic in Form Simplifying Square Roots That Contain Whole Numbers Dividing a Polynomial by a Monomial Writing Numbers in Scientific Notation Solutions to Linear Equations in Two Variables Solving Linear Inequalities Multiplying Two Mixed Numbers with the Same Fraction Special Fractions Solving a Quadratic Inequality Parent and Family Graphs Solving Equations with a Fractional Exponent Evaluating Trigonometric Functions Solving Equations Involving Rational Expressions Polynomials Laws of Exponents Multiplying Polynomials Vertical Line Test http: Solving Inequalities with Fractions and Parentheses http: Multiplying Polynomials Fractions Solving Quadratic and Polynomial Equations Extraneous Solutions Fractions

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Intercepts Given Ordered Pairs and Lines

When a line crosses one, or both, of the axes the point of the intersection is labeled â€œinterceptâ€.

All points on the y-axis have the first element of zero. The second element is a value of y where the line y = b intersects the line x = 0. The point is labeled as (0, b) and is called the y-intercept point. All points on the x-axis have the second element of zero. The first element is a value of x where the line x = a intersects the line y = 0. The point is labeled as (a, 0) and is called the x-intercept point.

1. For the equation 2x − 3y = 6 complete the two points below.

2x − 3(0) = 6, x = 3 2(0) − 3y = 6, y = - 2

( 3 , 0 ) and ( 0 , -2 )

If both the x-intercept and the y-intercept are integers, we can place them in the middle of the table. Then we can find the difference in the x-values for dx and the difference in the y-values for dy and use these differences to build arithmetic sequences for the table.

 Let x = 0, then 2( 0 ) − 3y = 6 or y = -2 which gives the point: ( 0 , -2 ) Let y = 0, then 2x − 3( 0 ) = 6 or x = 3 which gives the point: ( 3 , 0 ) Check the dy and dx on your table. Now you must CHECK the top and bottom points in the table to be sure that they are points on the line:

For the point (- 3, - 4) replace x = - 3 and y = - 4 in the given equation 2x − 3y = 6

CHECK: For the point (9, 4) replace x = 9 and y = 4 in the given equation 2x − 3y = 6

CHECK:  2. For the equation 2x + 5y = 10 complete the two intercept points below.

2x + 5(0) = 10, x = 5 2(0) + 5y = 10, y = 2

( 5 , 0 ) and ( 0 , 2 )

Plot the points and draw the line through the points.. Put the points on the table below, find the differences dx and dy between the two points. Use these differences to complete the table of arithmetic sequences. Work in the space below:

Check top and bottom points:

2(- 5) + 5y = 10, y = 4

2(10) + 5y = 10, y = -2 Looking at this line from left to right describe how the points â€œstepâ€ or line â€œslantsâ€ up or down?

Sometimes we encounter a problem where we solve Ax + By = C for y to find intercepts and neither one is an integer.

3. Graph 3x â€“ 5y = 7. All of the numbers are prime and have no common factors.

Note: If x = 0 then and if y = 0 then . Points: Since neither of these is an integer it will be difficult to use the x-intercept or y-intercept to draw the graph. We need to find integers as coordinates for the starting point.

If we solve the literal equation for y we get Let us examine the equation Now, let us again turn to LOGIC: We know that we will get an integer for y if we find a replacement value for x that will make the sum of the numerators a multiple of 5.

Since - 3 − 7 = -10 we will choose x = -1: Again, since 12 − 7 = 5 we will choose x = 4: Now we have starting points with integers: ( -1, -2 ) and (4, -1) . We can plot the points then: Start at (-1, -2) and note the move up 3 and right 5 to the next point (4, -1) and repeat the move or down 3 -- left 5 find more points and draw the line New points ( - 6, - 5 ) ( 9, 4 )