2.4 W RITING L INEAR F UNCTIONS Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Objectives.

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Presentation transcript:

2.4 W RITING L INEAR F UNCTIONS Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Objectives Point-slope form Vocabulary Last class we did...

Example 1: Writing the Slope-Intercept Form of the Equation of a Line Write the equation of the graphed line in slope-intercept form. Step 1 Identify the y -intercept. The y -intercept b is 1. Step 2 Find the slope. Choose any two convenient points to find slope. Slope is = = –. rise run – –4 4 –3 Step 3 Write the equation in slope-intercept form. y = mx + b 3434 y = – x + 1 m = – and b = The equation of the line is

Write the equation of the graphed line in slope-intercept form. Check It Out! Example 1

Example 2A: Finding the Slope of a Line Given Two or More Points Find the slope of the line through (–1, 1) and (2, –5): Let ( x 1, y 1 ) =(–1, 1) & ( x 2, y 2 ) = (2, –5). Use the slope formula. The slope of the line is –2.

Example 2B: Finding the Slope of a Line Given Two or More Points Find the slope of the line. x y Choose any two points. Find the slope of the line shown. Example 2C: Finding the Slope of a Line Given Two or More Points Choose any two points.

Example 3: Writing Equations of Lines In slope-intercept form, write the equation of the line that contains the points in the table. Remember always rewrite in slope-intercept form. x–8–4 48 y–5–3.5–0.51

Example 4A: Linear Entertainment Application The table shows the rents and selling prices of properties from a game. Selling Price ($) Rent ($) Express the rent as a linear function of the price. Let x = selling price and y = rent. Find the slope by choosing two points. Let ( x 1, y 1 ) be (75, 9) and ( x 2, y 2 ) be (90, 12). To find the equation for the rent function, use point-slope form. Use the data in the first row of the table. Simplify. y – y 1 = m ( x – x 1 )

Example 4B: Entertainment Application Graph the relationship between the selling price and the rent. How much is the rent for a property with a selling price of $230? Substitute. The rent for the property is $40. y = 46 – 6 y = 40 ItemsCost ($) Express the cost as a linear function of the # of items. Check It Out! Example 4a To find the rent for a property, use the graph or substitute its selling price of $230 into the function.

Example 5A: Writing Equations of Parallel and Perpendicular Lines Parallel lines have equal slopes. Use y – y 1 = m(x – x 1 ) with (x 1, y 1 ) = (5, 2). Distributive property. Simplify. m = 1.8 y – 2 = 1.8( x – 5) y – 2 = 1.8 x – 9 y = 1.8 x – 7 Write the equation of the line in slope-intercept form. parallel to y = 1.8 x + 3 and through (5, 2) Example 5B: Writing Equations of Parallel and Perpendicular Lines Write the equation of the line in slope-intercept form. perpendicular to and through (9, –2)