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slope & y-intercept. Edited version of kballard @ math.weebly.com. Vocabulary. A rate of change is a ratio that compares the amount of change of a dependent variable to the independent variable. Slope : the steepness of a line described by rate of change of y and x. Steepness of Lines.
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slope & y-intercept Edited version of kballard @ math.weebly.com
Vocabulary • A rate of change is a ratio that compares the amount of change of a dependent variable to the independent variable. • Slope: the steepness of a line described by rate of change of y and x.
Steepness of Lines The slope of a line is a measure of its steepness. Use absolute value to compare the steepness of multiple lines.
What does slope look like? • There are four types of slope that describe the rate of change. • Using this will help you check your work and describe your linear equation.
Slope Formula • If you do not have a graph, but want to find the slope, you can use two points in the slope formula. • Substitute in both points • Subtract and simplify
Slope-Intercept Form The linear equation y = mx + b is written in slope-intercept form. x and y stand for any x and y value. mis theslope(rise over run) b is the y-intercept (on the y-axis) y = mx + b
Identify slope and y-intercept y= mx + b m is always slope b is always the y-intercept Look at each equation and determine the slope value and the y-intercept value. • y = 4x + 5 • y = ½ x – 7 • y = x – ¾ • y = -x + 3 • y = x • y = 4 • x = 2
Identify slope and y-intercept y = mx + b If you have the graph, Find the y-intercept Count rise over run Write the equation
Write the linear equation. Write the equation in slope-intercept form. y = mx + b
Graphing a line. Slope-intercept form is the easiest way to graph a line when you have an equation. It is the main way that lines are expressed. Y = x + 2
Describing Slope -EX Tell whether the slope of each line is positive, negative, zero, or undefined.
Finding Slope from a Graph-Ex • To find the slope from a graph, • Pick any two points on the line. • Count RISEover RUN and simplify
Practice • Name the type of slope and find the slope.
Practice • Find the slope of each line.
Graph Lines #1 • How will we graph a line when we have y=mx + b? Example: y = 2/3x - 4 m= _____ b = _______ • Plot the y-intercept • Use your slope to count rise over run • Connect the dots!
Graph Lines #2 • How will we graph a line when we have y=mx + b? Example: y = -3x + 2 m= _____ b = _______ • Plot the y-intercept • Use your slope to count rise over run • Connect the dots!
Graph Lines #3 • How will we graph a line when we have y=mx + b? Example: y = 1 m= _____ b = _______ • Plot the y-intercept • Use your slope to count rise over run • Connect the dots!
Graph Lines #4 • How will we graph a line when we have y=mx + b? Example: x = -3 m= _____ b = _______ • Plot the y-intercept • Use your slope to count rise over run • Connect the dots!
Graph Lines Identify the slope and y-intercept, then graph the linear equation. y = 2x + 3 y = -½x - 1 y = 5/6x + 8 y = x - 7
REVIEW • What is rate of change? • What is slope? • What are the four types of slope? • What does “rise” represent? • What does “run” represent? • How do you find slope from a graph? • What is the slope formula?
Review What is slope-intercept form? What do m and b represent? How do you graph a line with slope-intercept form? What are the two special cases?
MATH HUMOR • How are linear functions similar to Cupid? • They have a partner for every number. • Teacher: Where’s the graph of your function? • Student: It was intercepted on the way to school. • Why were the math students getting up and sprinting around the classroom? • Their teacher kept saing “rise” and “run” • Why was the scientist smiling as he worked? • His graph had a great plot!
