Warm Up Oct. 11 th 1. 2. 3. Evaluate for x = 3 and y = −2. a. 2x − 5 b. 3y + 4x.

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Presentation transcript:

Warm Up Oct. 11 th Evaluate for x = 3 and y = −2. a. 2x − 5 b. 3y + 4x

Slope Also known as “rate of change” or “linear change” Definition: The slope of a line tells you the steepness of a line. The symbol for slope is "m". Slope is the ratio of the change in y to the change in x, where (x 1, y 1 ) and (x 2, y 2 ) are coordinates. Slope is usually a fraction, so make sure you REDUCE!

Positive Slope:Negative Slope: When m > 0When m < 0 Slope of 0 or No Slope: Undefined Slope: When m = 0

Finding Slope from a Graph Determine the slope from each graph below

You Try! 2. Find the slope between the points (-8, 0) and (4, 2). 3.Find the slope between the points (12, 5) and (3, 5). 4. Find the slope between the points (-7,10) and (-7,1).

Missing Coordinates Examples: 1. Find the value of r so that the line through (10, r) and (3, 4) has a slope of.

Missing Values Examples: 1. Find the value of r so that the line through (2, 8) and (r, -4) has a slope of -3.

3. Determine the value of r so that the line that passes through (5, r) and (2, -3) has a slope of. You Try!

Rate of Change - Another phrase for slope Examples: 1.SALESA magazine had 14,625 subscribers when it began publication. Ten years later it had 11,135 subscribers. What is the average yearly rate of change in the number of subscribers for the ten-year period?

Examples: 2.SALARY In 1991, the minimum wage rate was $4.25 per hour. In 1997, it was increased to $5.15. Find the annual rate of change in the minimum wage rate from 1991 to 1997.

3. Margo went to the lumber yard to buy supplies to build a ramp. She knows that they will need many pieces of wood. Each piece of wood costs $3. a) Write a function, f(x), for the total cost of the wood pieces if Margo buys x pieces of wood. b) Make an input/output table of ordered pairs and then graph the function.

c) What is the slope of the line that you graphed? d) How does the slope of this line relate to the situation with the pieces of wood? e) Is there a relationship between the slope of the line and the equation of the line? If so, describe that relationship. f) How much will 23 pieces of wood cost? g) How many pieces of wood can she buy for $117?

Homework 5.1 Practice Worksheet Odds

Exit Ticket On a blank sheet of paper, answer the following questions: 1.What is the slope of the line containing the points (-2, -5) and (7, 8)? 2.Find the value of r so that the line containing the points (-3, -4) and (-5, r) has a slope of -9/2 3.Jazsmin is driving to Disney World. At 7 o’clock, she is 400 miles away. At 11 o’clock, she is 250 miles away. What is her rate of change per hour? (Speed)