PPT-5.1: Rate of Change and Slope

Rate of change Shows the relationship between two VARIABLE quantities The table shows the elevation of a hang glider over time Is the rate of change in elevation with respect to time constant What does the rate of change represent. Section . 3.3. Rates of Change. Average vs. Instantaneous Rates. Average Speed. The concept of speed (distance traveled divided by time traveled) is a familiar instance of a . rate of change. .. Example: To drive the 15.5 miles from Clayton State to Turner field, it takes 18 minutes.. Ratios. A . ratio. is a comparison of . two. numbers.. Example: Tamara has 2 dogs and 8 fish. The ratio of dogs to fish can be written in three different ways. ..  .  . ***. Be careful with the . Tangent Lines. Average Rate of Change. The . average rate of change. of a quantity over a period of time is the slope on that interval of time.. Ex.:. . Find the average rate of change of . f(x) = x. Standard: . 8.EE.B.. 6 . Use . similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.. Slope is the rate of change . or. . . Secant slope. the slope between two points. . tangent slope. the slope at one point of contact. and is based upon a limit.. Noun: derivative. Verb: differentiation or to. Ratios. A . ratio. is a comparison of . two. numbers.. Example: Tamara has 2 dogs and 8 fish. The ratio of dogs to fish can be written in three different ways. ..  .  . ***. Be careful with the . Standard: . 8.EE.B.. 6 . Use . similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx b for a line intercepting the vertical axis at b.. Standard:. MAFS.912.S-ID.3.7. : . Interpret . the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.. . Problem of the Day:. Solve for the slope between (-1,-5) and (6,9. Objective: SWBAT determine the slope of a line given a graph or two ordered pairs.. Mini Quiz 39. Find the domain and range of the function:. 2. What is the greatest value in the range of y=2x 4 for the domain {-2, -1, 0, 1}. NOW: . Replace: . Graph of . , with words:. Graph: (. , the . slope of the tangent line to the . function . . at that . point). .  . CALCULUS problem:. Graph: (. , the slope of the tangent line to the function . Graph . Equations of Lines. Objectives:. To find the slope of a line given 2 points. To classify a line based on its slope. To find the slope of parallel and perpendicular lines. To graph the equation of a line using slope-intercept and standard form of a line. October 17-18, 2016. Mrs. Agnew. Essential Question. How do you find the average rate of change of . a function?. Essential Vocabulary. Average Rate of Change. Function. Function Notation. Average Rate of Change. 2. Differentiation is all about measuring change! . Measuring change in a linear function:. . y = a + bx. a. = intercept. b. = constant slope i.e. the impact of a unit change in x on the level of y. HMS Scaler-based Fall ‘18 Boiling Slopes . D. Mack. 10/28/20. Abstract. Using Hem’s scaler reports from the Fall ‘18 . lumi. scan, I get boiling slopes for C, LH2, and LD2 with total errors of ~+-0.3% . Results are consistent between the 2 pre-triggers .