Name_______________________________ 3-4 Ticket In

Geometry Period_____ Date______

Ticket in the Door!

After watching the assigned video and learning how to determine the slope given two points using the slope formula, answer the following question.

a. Determine the slope of a line through the points (−2,4) and (1,2)

b. What would the equation of the line be in point slope form?

Name_______________________________ Date__________

Geometry Period_______ Notes 3-4

Lesson 3-4: Slope!!

Learning Goal:How do you determine the slope and the equation of a line when given two points on

that line?

*We need to find the slope when we have two points on the line (we don't have the equation of the line).

Point 1 (x1, y1) Point 2 (x2, y2)Method 1

GraphicallyMethod 2Slope Formula ( yes –we MUST know this formula)

Very Important: Slope is ALWAYS, change in y over change in x

Tips for Success: Slope

1) Simplify your fractions 2) Watch out for double negatives 3) Change in y over

change in x

4) Negative fraction come in many forms 5) Label points x1, y1 and x2, y2

Let's Apply It!Given quadrilateral ABCD, with points A(−7 ,5) , B(−4 ,8), C (−1 ,5) and D(−5 ,0).

Find the slope of each side of the quadrilateral.

What can you infer about the sides AB and BC?

Self-Assess for success! Where do you rank yourself today???

Rank #:

Name: ______________________________________ 3-4 Practice B

Geometry Pd. _______ Date: ____

1) Find the slope of the line that passes through the points (−9 ,−8) and (1 ,−4) . Simplify your slope!

2) Write the equation of the line that passes through the points (−7 ,2) and (5,5) .

3) Quadrilateral MATH has the coordinates (−3 ,4 ), A(2,4 ), T (1 ,7) , and H (−4 ,7). Find the slope of each side. What inferences can you make based on the slopes?

-make sure you simplify your answer!

Steps to SolveAsk yourself: 1) What do I need in order to write the equation of a line?2) How can I find slope?3) How can I find a y-intercept?

What is a quadrilateral?

Find 4 separate slopes make sure you include

each point!. What do you see?

4) Error Analysis: Find the mistake in the student’s work below. DESCRIBE the mistake and then FIX the mistake.

5) Triangle ABC has vertices with ( x ,3 ) , B(−3 ,−1) , and C (−1 ,−4). Determine and state a value of x that would make triangle ABC a right triangle. Justify why ∆ ABC is a right triangle . [The use of the set of axes below is optional.]

Solve for the slope of BC

Then m⊥!

Given that B is the right angle

From B count the slope until you

reach a y-value of 3

State the coordinate of A

6) The line that passes through point (2 , −5 ) and (4 , y )has a slope of 3 . Find y.

7) Find the slope of the following in simplest form

(3a ,5b) and (−6 a ,8b)

8) Given MN shown below, with M (−6,1) and N (3 ,−5), what is an equation of the line that passes through point P(6,1) and is parallel to MN?

1)

2)

3)

4)

9) The slope of QR is x−1

4 and the slope of ST is 83 . If QR⊥ ST , determine and state the value of x

Keep a and b in the formula! Combine like terms then

simplify

10) State whether the lines represented by the equations y=xandy+3=−(x+11) are parallel, perpendicular, or neither. Justify your answer.

11) Making Predictions… Write the equation of the perpendicular bisector of segment A(-4,-6) and B(8,6).

a) If we know its perpendicular, we can get the slope for this line: Solve it!

b) If it’s a bisector that means it must travel through the ____________________ of segment AB

Do we know how to solve that yet?

c) If I told you the midpoint is (2 ,0), state the equation of the perpendicular bisector:

Look at the slopes!!!!!

Name: ______________________________________ 3-4 Practice A

Geometry Pd. _______ Date: ____

1) Find the slope of the following in simplest form

(3a ,5b) and (−6 a ,8b)

2) Quadrilateral MATH has the coordinates M (−3 ,4 ), A(2,4 ), T (1 ,7) , and H (−4 ,7). Find the slope of each side.

What inferences can you make based on the slopes?

3) Triangle ABC has vertices with ( x ,3 ) , B(−3 ,−1) , and C (−1 ,−4). Determine and state a value of x that would make triangle ABC a right triangle. Justify why ∆ ABC is a right triangle . [The use of the set of axes below is optional.]

4) The line that passes through point (2 , −5 ) and (4 , y ) has a slope of 3 . Find y.

5) Given MN shown below, with M (−6,1) and N (3 ,−5), what is an equation of the line that passes through point P(6,1) and is parallel to MN?

6) The slope of QR is x−1

4 and the slope of ST is 83 . If QR⊥ ST , determine and state the value of x

7) State whether the lines represented by the equations y=xandy+3=−(x+11) are parallel, perpendicular, or neither. Justify your answer.

1)

2)

3)

4)

8) In the coordinate plane, the vertices of are , , and . Prove that is a right triangle.

State the coordinates of point P such that quadrilateral RSTP is a rectangle. (Adjacent sides are perpendicular)

9) Making Predictions… Fill in: A perpendicular bisector is a line that forms a _____________________ with a given line segment and travels through the ________________________ of that segment.

Write the equation of the perpendicular bisector of segment A(-4,-6) and B(8,6).

What part of the equation CAN you solve for? What additional information do you need to know in order to complete this equation?

Challenge Corner

1.

A)

B)

A) Answer

B) Answer