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Algebra 1 Bell Ringer Find the slope of the line that passes through the points. 1. (2, –1), (4, 0) 2. (–1, –3), (1, 5) 3. A landscape architect charges $75 for a consulting fee and $30 per hour. Write an equation that shows the cost C as a function of time t (in hours). Chapter 5 Writing Linear Equations Prerequisite Skills Page 280: 1-9 5-1 Objective: Write Linear Equations in Slope-Intercept Form Review of Lingo • Y-intercept • Slope • Slope-Intercept Form Slope Intercept Form • y = mx + b • m = slope • b = y-intercept Use Slope and Y-intercept to Write an Equation • Just plug it in! • Write an equation of the line with a slope of 3 and a y-intercept of 5. • What would the graph look like? EXAMPLE 1 Use slope and y-intercept to write an equation Write an equation of the line with a slope of –2 and a y-intercept of 5. y = mx + b Write slope-intercept form. y = –2x + 5 Substitute –2 for m and 5 for b. Question • What if you had to write an equation just by looking at the graph? How would you do it? EXAMPLE 2 Standardized Test Practice Which equation represents the line shown? The slope of the line is rise = –2 = – 2 . run 5 5 The line crosses the y-axis at (0, 3). So, the y-intercept is 3. Write slope-intercept form. y = mx + b y=– 2 x+3 5 Substitute – 2 for m and 3 for b. 5 GUIDED PRACTICE for Examples 1 and 2 Write an equation of the line with the given slope and y-intercept. 1. Slope is 8; y-intercept is –7. ANSWER y = 8x – 7 GUIDED PRACTICE for Examples 1 and 2 Write an equation of the line with the given slope and y-intercept. 2. Slope is 3 ; y intercept is –3. 4 3x–3 ANSWER y= 4 More Examples • Page 286: 11, 12 Using Two Points • If you know where the y-intercept is and any other point on the line, then you can write an equation of the line. • How? EXAMPLE 3 Write an equation of a line given two points Write an equation of the line shown. EXAMPLE 3 Write an equation of a line given two points SOLUTION STEP 1 Calculate the slope. STEP 2 y –y –1 – (–5) 4 m = x2 – x1 = = 3–0 2 1 3 Write an equation of the line. The line crosses the y-axis at (0, –5). So, the y-intercept is –5. y = mx + b Write slope-intercept form. y= 4 x–5 3 Substitute 4 for m and 5 for b. 3 More Examples • Guided Practice #3 on bottom of page 284 • Page 287: 23 Function Notation • Review of Function Notation Evaluate f(x) = 2x + 1 when x = 3 f(3) = 2(3) + 1 f(3) = 7 *This represents the point (3, 7) Practice • f(x) = 2x – 3 when x = 7, what point would this be? • f(x) = ½x – 7 when x = -6, what point would this be? Question • If you only see f(0) = 5 what point is this and why is it so valuable? Example • Write an equation for the linear function f with the values f(0) = -2 and f(3) = -6 Example • Write an equation for the linear function f with values f(0) = 4 and f(9) = 10. EXAMPLE 4 Write a linear function Write an equation for the linear function f with the values f(0) = 5 and f(4) = 17. SOLUTION STEP 1 Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17). STEP 2 Calculate the slope of the line that passes through (0, 5) and (4, 17). y2 – y1 m= x2 – x1 = 17 – 5 4–0 12 = 4 =3 EXAMPLE 4 STEP 3 Write a linear function Write an equation of the line. The line crosses the y-axis at (0, 5). So, the y-intercept is 5. y = mx + b Write slope-intercept form. y = 3x + 5 Substitute 3 for m and 5 for b. ANSWER The function is f(x) = 3x + 5. GUIDED PRACTICE 3. for Examples 3 and 4 Write an equation of the line shown. ANSWER y=– 1 x+1 2 GUIDED PRACTICE 4. for Examples 3 and 4 Write an equation for the linear function f with the given values. f(0) = –2, f(8) = 4 ANSWER y= 3 x–2 4 GUIDED PRACTICE 5. for Examples 3 and 4 Write an equation for the linear function f with the given values. f(–3) = 6, f(0) = 5 ANSWER y = – 13 x + 5 Real-World Situations • Remember key words: per, for each, for every…, etc., tells you to multiply. In this section, this will represent your slope. Example • The YMCA charges an initial membership fee of $45 and $60 per month to work out in the gym. Write an equation that gives the total cost of being a member and working out every month. Find the amount you would spend if you worked out every month for a year. Look over Example 5 Homework • 1, 2 – 36 ev, worksheet bonus 44, 52