Lesson 2 7 Core Focus on Linear Equations
- Slides: 12
Lesson 2. 7 Core Focus on Linear Equations Calculating Slope From Graphs
Warm-Up Write each fraction in simplest form. Do not convert to mixed numbers. 1. 4. 2. 5. 3.
Lesson 2. 7 Calculating Slope From Graphs Use slope triangles to find the slope of lines.
Vocabulary Slope The ratio of the vertical change to the horizontal change in a linear graph. Like rate of change, slope is used to describe the steepness of a line. Good to Know! A line can have a slope that is positive, negative, zero or undefined. Slope Triangle A right triangle where one leg of the triangle represents the vertical rise and the other leg is the horizontal run in a linear graph.
Finding Slope The slope of a line is the ratio of the change in y-values to the change in x-values.
Example 1 Draw a slope triangle for the line and identify the slope of the line. a. b. +2 – 1 +2 +2
Example 1 Continued… Draw a slope triangle for the line and identify the slope of the line. c. +3 d. +3
Example 2 Graph the line that goes through the given points, draw a slope triangle and give the slope. a. x y 2 7 5 1 Graph the points. Draw the slope triangle. Start at the point furthest to the left. Determine the lengths of the legs of the triangle. – 6 +3
Example 2 Continued… Graph the line that goes through the given points, draw a slope triangle and give the slope. b. (0, 1) and (2, 4) +2 Graph the points. Draw the slope triangle. Start at the point furthest to the left. +3 Determine the lengths of the legs of the triangle.
Example 3 Graph a line with a slope of 2. When a slope is given without a denominator, it is mathematically correct to place a 1 in the denominator. This does not change the value of the slope. No y-intercept was given so put a point anywhere on the graph. The slope of 2 can be written as +1 . From the point, rise +2 and run +1. Graph the line the crosses through the two points on the graph. +2
Communication Prompt How do you find the slope of a line from a graph?
Exit Problems Is the slope of each line positive, negative, zero or undefined? 1. Positive 2. Undefined 3. Negative 4. Zero