Writing Equations with Slope and a Point Unit

Writing Equations with Slope and a Point Unit 4 Lesson 2

There are three different forms to write linear equations • Point Slope Form • Slope Intercept Form • Standard Form Based on their names, what do you think the equations might look like?

Point Slope Form Reflection Questions: • What do you notice when you look at point slope form? • • Why do you think Point Slope form works?

Why does point slope form work? Now let’s start writing equations in point slope form!

Example 1 •

Example 2 •

Example 3 A hot air balloon is descending at a rate of 2. 5 meters per second. The balloon is at a height of 590 meters after 30 seconds. Write the equation in point slope form to represent the path of the air balloon. Reflection Question: What key words help you recognize what the independent an dependent variables are?

What if the point we are given is the y intercept? • Reflection Question: What do you notice if you solve your points slope form equation for y?

Slope intercept form Example 5: Given a slope of -3 and the point (5, -8), write the linear equation An y. I de as? ?

Example 6 Water pressure can be measured in atmospheres (atm). As you increase your depth in the water, the pressure increases 0. 1 atm per meter. At a depth of 10 meters, the pressure is measured to be 1 atm. Write the equation of this relationship in slope intercept form.

Standard Form • A and B are called COEFFICIENTS • C is the CONSTANT Why do we think Standard Form might be useful? ? What is the difference between a coefficient and a constant? If we aren’t given the SLOPE Helps us find intercepts quickly

Example 7 What are the x and y intercepts of 5 x – 6 y = 60? REMEMBER: X intercept – when Y is ZERO Y intercept – when X is ZERO

Example 8 and 9 •

Example 10 A media download store sells songs for $1 each and movies for $12 each. You have $60 to spend. Write and graph an equation that describes the items you can purchase

Writing equations with two points Unit 4 Lesson 4

How can we use two points to write equations? Any Ideas? We can… • Use two points to find Slope • Use one point to find missing pieces

Example 1 What is the equation of the line that passes through (-2, -3) and (1, 4) in Slope intercept, point slope, and Standard form?

Example 2 The table shows the number of gallons of water in a tank after a certain number of hours. The relationship is linear and you need to find the equation in Standard form

Example 3 – Do the problem assigned to your group! • What do you notice about some of the equations?

Example 4 •

Example 5 Find the x and y intercepts of the line that passes through (3, -8) and (-4, 13)

Ticket to Homework – Compare and Check •

Linear Inequalities Unit 4 Lesson 7

Carpentry You budget $200 for wooden planks for outdoor furniture. Cedar costs $2. 50 per for and pine costs $1. 75 per foot. Write an inequality that shows how much each type of wood can be bought. What are three possible amounts of each type of wood that can be bought within your budget? Write Inequality Graph on Calculator for possible Solutions

Parallel and Perpendicular Lines Unit 4 Lesson 9

In Summary from Geogebra… •

Example 1 A line passes through (-3, -1) and is parallel to the graph y=2 x+3. Write the equation that represents the line in slope intercept form.

Example 2 •

Example 3 •

Example 4

Example 5 You are being asked to prove that Birch street and Fir street are not perpendicular. How can you justify your response?

Ticket to Homework- Compare and Check • 4) Prove that ABCD is a rectangle using properties of parallel and perpendicular lines. Explain your reasoning

Scatter Plots – Associations and Line of Fit Unit 4 Lesson 11

Steps to find equation of trend line • Graph data in coordinate plane. • Decide if there is an linear association • Draw a line that seems to pass close to MOST of the data points • Use two points on the line of fit to write an equation

Example 1: Find the equation of the trend line that represents the price of several bulk grains Using your equation, predict the cost of 35 ounces of bulk grains

Example 2 Find the equation of the trend line in standard form

Example 3

Scatter Plots and Line of Fit Unit 4 Lesson 12

VOCABULARY TIME! • INTERPOLATE What do yo u thin words k thes e mean ? Estimating a value between known values • EXTRAPOLATE Estimating a value outside the range of known values

It’s all about making predictions! w lues a v n kno n e twe Be w e sid Out no k f o es u l a nv

Example 1 Find the equation of the trend line Make a statement of interpolation Make a statement of extrapolation

Example 2 Find the equation of the trend line Make a statement of interpolation Make a statement of extrapolation

Reflection Question In the previous example, why do we need to consider our domain and range restrictions when making a statement of extrapolation

Linear Regression and correlation coefficient Unit 4 Lesson Thirteen

What is a correlation coefficient and what does it mean? ? ? Correlation Coefficient

Let’s look at an example from yesterday using the Calculator! What does all this mean? Was our answer yesterday wrong?

Let’s look at an example from yesterday using the Calculator! What does all this mean? Was our answer yesterday wrong?