2.6. Slope-Intercept Form Working Under Pressure. My My Notes ACTIVITY

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Slope-Intercept Form SUGGESTED LEARNING STRATEGIES: Shared Reading, Marking the Tet, Questioning the Tet, Visualization, Create Representations, Think/Pair/Share, Note Taking M M Notes ACTIVITY.

As a diver swims deeper into the water, the pressure on the diver s bod increases at a rate of about atmosphere of pressure per 0 meters of depth.

1 Slope-Intercept Form SUGGESTED LEARNING STRATEGIES: Shared Reading, Marking the Tet, Questioning the Tet, Visualization, Create Representations, Think/Pair/Share, Note Taking M M Notes ACTIVITY. When a diver descends in a lake or ocean, pressure is produced b the weight of the water on the diver. As a diver swims deeper into the water, the pressure on the diver s bod increases at a rate of about atmosphere of pressure per 0 meters of depth. The table and graph below represent the total pressure,, on a diver given the depth,, under water in meters pressure (atm depth under water (meters. Write an equation describing the pressure eerted on a diver when under water. CONNECT TO SCIENCE Pressure is the measure of a force against a surface, and is usuall epressed as a force per unit area. Atmospheric pressure is defined using the unit atmosphere. atm is.9 pounds per square inch. ACADEMIC VOCABULARY A linear equation is an equation of the form A + B = C where A, B, and C are constants and A and B cannot both be zero. 00 College Board. All rights reserved.. What is the slope of the equation of the line that ou found? What are the units of the slope?. What is the -intercept of the line? Slope-Intercept Form of a Linear Equation = m + b where m is the slope of the line and b is the -intercept.. Identif the slope and -intercept of the line described b the equation = Linear equations can be written in several forms. ACADEMIC VOCABULARY The -intercept of a line is the -coordinate of the point where the line crosses the -ais, which is when the -coordinate is 0. Unit Linear Functions

2 ACTIVITY. Slope-Intercept Form M Notes SUGGESTED LEARNING STRATEGIES: Create Representations, Quickwrite, Group Presentation, Note Taking. Create a table of values for the equation = T hen plot the points and graph the line Eplain how to f ind the slope from the table. 7. Eplain how to f ind the -intercept from the table. 8. Eplain how to f ind the slope from the graph. 9. Eplain how to f ind the -intercept from the graph. EXAMPLE Write the equation, in slope-intercept form, of the line that passes through the point (, and has a slope of -. Step : Find the -intercept b substituting the coordinates of the point and the slope in the equation. = m + b = -( + b Substitute - for m, for, = - + b and for. + = - + b + 7 = b The -intercept is 7. Step : Substitute the slope and -intercept into the slope-intercept form. = m + b = Solution: = College Board. All rights reserved. SpringBoard Mathematics with Meaning Algebra

3 Slope-Intercept Form ACTIVITY. SUGGESTED LEARNING STRATEGIES: Create Representations, Self/Peer Revision, Note Taking TRY THESE A a. Write the equation, in slope-intercept form, of the line with a slope of and a -intercept of. M Notes b. Find the equation, in slope-intercept form, of the line that passes through the point (-, 7 and has a slope of -. c. Write an equation of the line shown in the graph at the right College Board. All rights reserved. Point-Slope Form of a Linear Equation - = m( - where m is the slope of the line and (, is a point on the line. You get this form of the equation b solving the slope formula m = - - for -, b multipling both sides b -. T he variable is the dependent variable, and is the independent variable. You ma use this form when ou know a point on the line and the slope. EXAMPLE Write an equation of a line with a slope of that passes through the point (,. Step : Substitute the given values into point-slope form. - = m( - - = ( - Step : Solve for. = ( - + Solution: = ( - + CONNECT TO AP In calculus, the point-slope form of a line is used to write the equation of the line tangent to a curve at a given point. If ou needed to epress the solution to Eample in slope-intercept form, ou could appl the distributive propert and combine like terms. Unit Linear Functions 7

4 ACTIVITY. Slope-Intercept Form M Notes SUGGESTED LEARNING STRATEGIES: Create Representations, Questioning the Tet, Marking the Tet, Note Taking, Think/Pair/Share TRY THESE B Find an equation of the line given a point and the slope. a. (-, 7, m = b. (, -, m = - c. (8,, m = -8 T he town of San Simon charges its residents for trash pickup and water usage on the same bill. Each month the cit charges a f lat fee for trash pick-up and a $0. per gallon usage fee for water. In Januar, one resident used gallons of water, and received a bill for $. 0. If is the number of gallons of water used during a month, and represents the bill amount in dollars, write a point (,.. What does the $0. per gallon represent?. Use point-slope form to write an equation that represents the bill cost in terms of the number of gallons of water used in a month.. Write the equation in Item in slope-intercept form. What does the -intercept represent? EXAMPLE Write an equation of the line that passes through the points (, and (,. Step : Find the slope b substituting the two points into the slope formula. m = - - = - Substitute (, for ( -, and (, for (,. m = - - = - = - Step : Substitute the slope and one of the points into point-slope form. = m( - - = - ( - Substitute (, for (, and - for m. = - ( - + Solve for. Solution: = - ( College Board. All rights reserved. 8 SpringBoard Mathematics with Meaning Algebra

5 Slope-Intercept Form ACTIVITY. SUGGESTED LEARNING STRATEGIES: Quickwrite, Look for a Pattern, Create Representations, Group Discussion Note Taking TRY THESE C a. Find the equation in point-slope form of the line shown in the graph. b. Find the equation in point-slope form of the line with a slope of that passes through the point (, -. c. Find the slope and a point on the line whose equation is = - ( +. d. Find the equation of the line that passes through the points (-, and (,. e. Write the equation of the line from Item (d above in slope-intercept form M Notes 00 College Board. All rights reserved. Standard Form of a Linear Equation A + B = C where A 0, A and B cannot both be zero, and A, B, and C are integers whose greatest common factor is one.. You can use the coefficients of this form of an equation to find the slope, -intercept and -intercept of a line. a. Write A + B = C in slope-intercept form to find the slope. b. Find the -intercept. c. Find the -intercept.. Find the slope and -intercept of the line described b the equation + = 8. MATH TERMS The greatest common factor of two or more integers is the greatest integer that is a divisor of all the integers. ACADEMIC VOCABULARY The -intercept is the -coordinate of the point where a line crosses the -ais. Unit Linear Functions 9

ACTIVITY. Slope-Intercept Form M Notes SUGGESTED LEARNING STRATEGIES: Create Representations, Identif a Subtask. Write + = 8 in the slope-intercept form of an equation. - - - - - - - - - - - - 7.

6 ACTIVITY. Slope-Intercept Form M Notes SUGGESTED LEARNING STRATEGIES: Create Representations, Identif a Subtask. Write + = 8 in the slope-intercept form of an equation Given the equation = + of a line, write it in the standard form of a linear equation. 8. The table below and the graph to the left represent the equations of two different linear functions. a. Which represents the line with the greater slope? Eplain. b. Which represents the line with the greater -intercept? Eplain CHECK YOUR UNDERSTANDING Write our answers on notebook paper. Show our work.. Write the standard form of the equation of the line with a slope of 7 that passes through the point (,.. Write the equation - = in slope-intercept form.. Write the equation = - + ( + in slope-intercept form.. Write the equation in standard form of the line that is represented b the data in the table As a diver descends into fresh water, we have determined that for ever 0 meters of depth, the pressure on the diver increases b one atmosphere. Find the equation of the line representing this relationship if we know that when the diver is at a depth of meters, there is a pressure of. atmospheres.. MATHEMATICAL REFLECTION Rate ourself on a scale of to on our perceived understanding of equations of lines for Slope-intercept, Point-slope, and Standard forms of a line. The lower the rating the lower the level of understanding. What can ou do to bring our level of understanding to a higher level? 00 College Board. All rights reserved. 0 SpringBoard Mathematics with Meaning Algebra

Essential Question How can you describe the graph of the equation y = mx + b?

Essential Question How can you describe the graph of the equation y = mx + b? .5 Graphing Linear Equations in Slope-Intercept Form COMMON CORE Learning Standards HSA-CED.A. HSF-IF.B. HSF-IF.C.7a HSF-LE.B.5 Essential Question How can ou describe the graph of the equation = m + b?