Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Write an equation of a line from a graph

Advertisements

1. (1, 4), (6, –1) ANSWER Y = -x (-1, -2), (2, 7) ANSWER

SOLUTION EXAMPLE 3 Determine whether lines are perpendicular Line a: 12y = –7x + 42 Line b: 11y = 16x – 52 Find the slopes of the lines. Write the equations.

SOLUTION EXAMPLE 1 A linear system with no solution Show that the linear system has no solution. 3x + 2y = 10 Equation 1 3x + 2y = 2 Equation 2 Graph the.

Write an equation given the slope and y-intercept EXAMPLE 1 Write an equation of the line shown.

Example 1 Identifying Slopes and y-intercepts Find the slope and y -intercept of the graph of the equation. ANSWER The line has a slope of 1 and a y -intercept.

Solve an equation with variables on both sides

Directions: Solve the linear systems of equations by graphing. Use the graph paper from the table. Tell whether you think the problems have one solution,

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

Use intercepts to graph an equation

EXAMPLE 2 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.

Write decimal as percent. Divide each side by 136. Substitute 51 for a and 136 for b. Write percent equation. Find a percent using the percent equation.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

EXAMPLE 4 Classify and write rules for functions SOLUTION The graph represents exponential growth (y = ab x where b > 1). The y- intercept is 10, so a.

EXAMPLE 1 Solve a linear-quadratic system by graphing Solve the system using a graphing calculator. y 2 – 7x + 3 = 0 Equation 1 2x – y = 3 Equation 2 SOLUTION.

EXAMPLE 4 Find the zeros of a quadratic function Find the zeros of f(x) = x 2 + 6x – 7. SOLUTION Graph the function f(x) = x 2 + 6x –7. The x- intercepts.

Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 +

Write an equation given two points

3.5 Solving systems of equations in 3 variables

Write and graph a direct variation equation

EXAMPLE 2 Write a rule for the nth term a. 4, 9, 14, 19,... b. 60, 52, 44, 36,... SOLUTION The sequence is arithmetic with first term a 1 = 4 and common.

Write an equation given the slope and y-intercept EXAMPLE 1 Write an equation of the line shown.

Graph an equation in standard form

7 = 7 SOLUTION EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1.

Solve a radical equation

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Example 1 Find the intercepts of the graph of. Finding Intercepts 2 1 y = x – = x – = x 10 = x STEP 1 Let 0 and solve for x to find the.

WRITE EQUATIONS OF PARALLEL AND PERPENDICULAR LINES November 20, 2008 Pages

Solving quadratic equations by graphing. X Y I x² - 2x = 3 You have to rewrite the equation to find the vertex before you can graph this function Use.

Substitution Method: 1. Solve the following system of equations by substitution. Step 1 is already completed. Step 2:Substitute x+3 into 2 nd equation.

EXAMPLE 3 Write the standard equation of a circle The point (–5, 6) is on a circle with center (–1, 3). Write the standard equation of the circle. SOLUTION.

EXAMPLE 1 Identifying Slopes and y -intercepts Find the slope and y -intercept of the graph of the equation. a. y = x – 3 b. – 4x + 2y = 16 SOLUTION a.

3.6 Solving Absolute Value Equations and Inequalities

EXAMPLE 1 Identify slope and y-intercept Identify the slope and y- intercept of the line with the given equation. y = 3x x + y = 22. SOLUTION The.

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

EXAMPLE 1 Solve by equating exponents Rewrite 4 and as powers with base Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

EXAMPLE 2 Checking Solutions Tell whether (7, 6) is a solution of x + 3y = 14. – x + 3y = 14 Write original equation ( 6) = 14 – ? Substitute 7 for.

Solve an inequality using multiplication EXAMPLE 2 < 7< 7 x –6 Write original inequality. Multiply each side by –6. Reverse inequality symbol. x > –42.

Use the substitution method

WARM UP GRAPHING LINES Write the equation in slope- intercept form and then Graph. (Lesson 4.7) 1.3x + y = 1 2.x + y = 0 3.y = -4 3.

Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.

SOLUTION EXAMPLE 3 Determine whether lines are perpendicular Line a: 12y = – 7x + 42 Line b: 11y = 16x – 52 Find the slopes of the lines. Write the equations.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

EXAMPLE 1 Solve an equation with two real solutions Solve x 2 + 3x = 2. x 2 + 3x = 2 Write original equation. x 2 + 3x – 2 = 0 Write in standard form.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.

Do-Now Evaluate the expression when x = –3. –5 ANSWER 1. 3x

Writing Equations of a Line

Factor the expression. If the expression cannot be factored, say so.

3.3 – Solving Systems of Inequalities by Graphing

Solve a literal equation

Solve an equation by multiplying by a reciprocal

Writing Equations of a Line

Solve an equation with two real solutions

Solve Systems of Equations by Graphing

Solve a system of linear equation in two variables

3.5 Solving systems of equations in 3 variables

Solving Systems of Equations using Substitution

Solving One and Two Step Equations

EXAMPLE 1 Write an equation of a line from a graph

Graph 2x + 4y = 16 by finding the x and y intercepts.

Systems of Equations Solve by Graphing.

Solve an inequality using subtraction

Warm-Up Solve the system by graphing..

Integrated Math One Module 5 Test Review.

6-1 System of Equations (Graphing)

Objectives: To graph lines using the slope-intercept equation

Solving Linear Systems by Graphing

Presentation transcript:

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept of the graph of 2x + 7y = 28. Find the intercepts of the graph of an equation EXAMPLE 1 Solve for x. 2x + 7(0) = 28 x == x + 7y = 28

2(0) + 7y = 28 Find the intercepts of the graph of an equation EXAMPLE 1 To find the y- intercept, substitute 0 for x and solve for y. Write original equation. Substitute 0 for x. Solve for y. ANSWER The x- intercept is 14. The y- intercept is 4. 2x +7y = 28 y = 28 7 = 4

Find the x- intercept and the y- intercept of the graph of the equation. GUIDED PRACTICE for Example x + 2y = 6 ANSWER 2, 3

GUIDED PRACTICE for Example x – 2y = 10 Find the x- intercept and the y- intercept of the graph of the equation. ANSWER 2.5, –5

GUIDED PRACTICE for Example 1 3. –3x + 5y = –15 Find the x- intercept and the y- intercept of the graph of the equation. ANSWER 5, –3