EXAMPLE 5 Solve a multi-step problem LIBRARY

Slides:

Advertisements

Similar presentations

EXAMPLE 4 Solve a multi-step problem EVENT PLANNING

Advertisements

EXAMPLE 1 Write an equation of a line from a graph

Write an equation given the slope and a point

SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner.

EXAMPLE 4 Solve a multi-step problem Write an exponential growth model giving the number n of incidents t years after About how many incidents were.

Graphing Using Slope - Intercept STEPS : 1. Equation must be in y = mx + b form 2. Plot your y – intercept ( 0, y ) 3. Using your y – intercept as a starting.

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

Find the x-intercept To find the y-intercept, we must use 0 for x. Substitute x = 0 into 2x + 3y = 6 and solve for y: 2x + 3y = 6 2(0) + 3y = y.

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.

EXAMPLE 6 Solve a multi-step problem Job Earnings You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour.

Use intercepts to graph an equation

EXAMPLE 3 Write an equation for a function

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.

EXAMPLE 2 Graph an equation using slope-intercept form

Warm-Up Write an equation in standard form of the line that passes through the given point and has the given slope m or that passes through the two given.

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.

Standardized Test Practice EXAMPLE 4 ANSWER The correct answer is B. DCBA Simplify the expression 4(n + 9) – 3(2 + n). 4(n + 9) – 3(2 + n) = Distributive.

Standardized Test Practice

EXAMPLE 5 Solve a multi-step problem Recording Studio

Standardized Test Practice

EXAMPLE 7 Solve a multi-step problem Printing Costs You are creating brochures that promote your school’s sports events. You pay $20 for computer time.

Write an equation given two points

Write a quadratic function in vertex form

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

5.4 Write Linear Equations in Standard Form

SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner.

SOLUTION EXAMPLE 4 Graph an equation in two variables Graph the equation y = – 2x – 1. STEP 1 Construct a table of values. x–2–1 012 y31 –3–5.

4.1 Write Linear Equations in slope-intercept form

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.

1.4 Graph Using Intercepts

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.

EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form because the vertex is given.

Write Linear Equations in Standard Form

Students will be able to write a linear equation in standard form. ANSWER 1.(1, 4), (6, –1) y + 2 = 3(x + 1) or y – 7 = 3(x – 2) y – 4 = –(x – 1) or y.

Writing Equations of a Line. Various Forms of an Equation of a Line. Slope-Intercept Form.

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

EXAMPLE 4 Solving an Equation with a Fraction Photography You take 16 of the 24 pictures of a roll of film on your first day of vacation. At this rate,

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.

3.6 Solving Absolute Value Equations and Inequalities

Examples and Guided Practice come from the Algebra 1 PowerPoint Presentations available at

EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.

Example 2 Graphing Using Slope-Intercept Form 1

EXAMPLE 1 Apply the distributive property

Lesson 3.3 Graph Using Intercepts Essential Question: How do you graph linear equations using x and y intercepts? Common Core CC.9-12.F.IF.7a Graph.

EXAMPLE 3 Graph y = ab + k for 0 < b < 1 x – h Graph y = 3 –2. State the domain and range. 1 2 x+1 SOLUTION Begin by sketching the graph of y =, which.

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.

EXAMPLE 3 Use the quadratic formula y = 10x 2 – 94x = 10x 2 – 94x – = 10x 2 – 94x – 300 Write function. Substitute 4200 for y. Write.

SOLUTION EXAMPLE 3 Write an equation of a line Write an equation of the specified line. The y- coordinate of the given point on the blue line is –4. This.

EXAMPLE 2 Graphing Using Slope-Intercept Form The y -intercept is 3, so plot the point (0, 3).STEP 1 The slope is, so plot a second point by 1 2 STEP 2.

5.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Write Linear Equations in Standard Form.

Solve a multi-step problem EXAMPLE 5 Trip Expenses Your art club is planning a bus trip to an art museum. The cost for renting a bus is $495, and the cost.

EXAMPLE 6 Solve a multi-step problem An athlete throws a shot put with an initial vertical velocity of 40 feet per second as shown. a. Write an equation.

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.

4.3 Graphing Using Intercepts Objective: Graph a linear equation using intercepts.

Write a quadratic function in vertex form

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

Writing Equations of a Line

Solve an equation by multiplying by a reciprocal

Writing Equations of a Line

Solve an equation with two real solutions

Solve a system of linear equation in two variables

EXAMPLE 1 Write an equation of a line from a graph

Systems of Equations Solve by Graphing.

Writing Equations of a Line

Objectives: To graph lines using the slope-intercept equation

WARM UP 3 WRITING EQUATIONS Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. (Lesson.

Presentation transcript:

EXAMPLE 5 Solve a multi-step problem LIBRARY Your class is taking a trip to the public library. You can travel in small and large vans. A small van holds 8 people and a large van holds 12 people. Your class could fill 15 small vans and 2 large vans. Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill. a. b. Graph the equation from part (a). c. List several possible combinations.

Solve a multi-step problem EXAMPLE 5 Solve a multi-step problem SOLUTION a. Write a verbal model. Then write an equation. 8 s l p 12 + = Because your class could fill 15 small vans and 2 large vans, use (15, 2) as the s- and l-values to substitute in the equation 8s + 12l = p to find the value of p. 8(15) + 12(2) = p Substitute 15 for s and 2 for l. 144 = p Simplify. Substitute 144 for p in the equation 8s + 12l = p.

EXAMPLE 5 Solve a multi-step problem ANSWER The equation 8s + 12l = 144 models the possible combinations. b. Find the intercepts of the graph. Substitute 0 for s. 8(0) + 12l = 144 l = 12 Substitute 0 for l. 8s + 12(0) = 144 s = 18

EXAMPLE 5 Solve a multi-step problem Plot the points (0, 12) and (18, 0). Connect them with a line segment. For this problem only nonnegative whole-number values of s and l make sense. The graph passes through (0, 12), (6, 8), (12, 4), and (18, 0). So, four possible combinations are 0 small and 12 large, 6 small and 8 large, 12 small and 4 large, 18 small and 0 large. c.

EXAMPLE 5 Solve a multi-step problem GUIDED PRACTICE for Example 5 EXAMPLE 5 Solve a multi-step problem 7. WHAT IF? In Example 5, suppose that 8 students decide not to go on the class trip. Write an equation that models the possible combinations of small and large vans that your class could fill. List several possible combinations. 8s + 12l = 136; 17 small, 0 large; 14 small, 2 large; 11 small, 4 large; 8 small, 6 large; 5 small, 8 large; 2 small, 10 large ANSWER