KEY KNOWLEDGE STATEMENT: The equation of a line gives important information about the graph of the line. Linear equations in the form y = mx + b gives the slope and y-intercept of the line. It can also be used to find an equation of the line when other conditions such as slope and a point on the line are known. To write an equation of a line from the graph, identify the m and b values and plug them in the slope-intercept form.
Aim: What is slope-intercept form and how do we graph an equation using it?
Instructional Objective: SWBAT write the equation of a line in slope-intercept form as well as graph any linear equations given two points on the line or the slope and y-intercept.
NYS Standard: AG4, AG5, AA34, AA35
KNOWLEDGE:
Students will be able to retain and recall that: / SKILLS
Students will be able to:
1. A linear function is a function that graphs a non-vertical line.
2. A linear equation is an equation that models a linear function.
3. The slope-intercept form of a linear equation is y = mx + b where m = slope, b = y-intercept / 1. Identify the Slope and y-intercept
2. Determine the equation given a graph
3. Graphing an equation
Instructional Procedures
1. Salutation ( 2 min)
2. Do Now: 5 minutes
3. Share Out 5 min.
4. Mini-Lesson 1: Slope-Intercept form
5. Mini-Lesson 2: Writing equation of a line from
certain conditions
6. Practice Set (20 min)
7. Wrap Up/ Exit Slip (5)
Aim: What is slope-intercept form and how do we graph an equation using it?
Do Now: I. Calculate the slope. Remember given pointsand slope =
a. (-1, 0), (1, 10) b. (0, 3), (4, -9)
II. What is the slope of the line shown in the accompanying diagram?
A. -4/3 B. 4/3 C. ¾ D. -3/4
III. What is the slope of the line in the accompanying diagram?
A. 2/3 B. -2/3 C. 3/2 D. -3/2
Mini-Lesson 1: Slope-Intercept Form of a Line
What information do we kneed to know about a linear equation?
What do all of the graphs have in common? How are they different?
What do all of the graphs have in common? How are they different?
1. Given: y = -2x + 1
Fill the chart with y-values using the given x –values.
x / Y = -2x + 1 / y0
1
2
3
Using any two ordered-pairs, calculate the slope.
m =
Using the ordered –pairs on the table, graph the linear function.
Answer the following:
1. How can the slope you found be determined from the equation?
2. Where does the line intersect the y-axis? How is this value related to the equation of the line?
TO-WITH: IDENTIFYING SLOPE AND Y-INTERCEPT FROM EQUATION
Identify the slope and y-intercept of each linear equation.
Linear Equation / Slope (m) / Y –intercept (b)1. Y = 3 x + 2
2. y = x - ¾
3. y = - ¾ x + 2
TRY THIS! Identify the slope and y-intercept of each linear equation.
4. y = - x - 55. y = x - 1
6. y = - ½ x + 3
7. y = - x + 4
8. y = x - 3
WRITING THE LINEAR EQUATION GIVEN THE SLOPE and Y-INTERCEPT
Write an equation of the line with the given slope and y-intercept.
Slope / y-intercept / Equation1. m = 3/7 / 4
2. m = -4 / -3
3. m = -3/4 / 10
TRY THIS!
Slope / y-intercept / Equation4. m = -2/5 / -1
5. m = 1 / 5
6. m = -1/3 / 2
WRITING AN EQUATION FROM THE GRAPH
To write an equation of a line from the graph, do the following steps.
Step 1: Find any two points on the line.
Step. 2. Calculate slope from the two points.
Step 3. Find where the line intersects the y-axis.
Step. 4. Write an equation in slope intercept form.
TO-WITH: Write an equation of the line from the graph.
1) 2)
m = ______m = ______
b = ______b = ______
Equation: ______Equation: ______
TRY THIS!
1) 2)
m = ______m = ______
b = ______b = ______
Equation: ______Equation: ______
Mini-Lesson 2: WRITING AN EQUATION OF A LINE GIVEN SLOPE AND A POINT ON THE LINE.
Remember: In the linear equation y = mx + b, if b is NOT KNOWN, but the slope and a point on the line is known, we can find the equation of the line by doing these.
Step 1: Plug the given slope to m.
Step 2: Plug the first number in the ordered- pair to x and the second number in the
ordered-pair to y.
Step 3: Solve for b.
Step 4: Write the equation in the form y = mx + b.
TO-WITH:
Write an equation of the line with the given slope and point.
1. m = 3, point (2, 5) / 2. m = - 4 , point (-3, 1)TRY THIS!
Write an equation of the line with the given slope and point.
1. m = -2, point (-1, 1) / 2. m = 5, point (-2, -3)