Unit 5: Analytic Geometry Minds On. Unit 5: Analytic Geometry Learning Goals: I can define slope I can determine the slope and the y- intercept of.

Unit 5: Analytic Geometry

Minds On

True or False? Explain your Reasoning.

a) = =

b) = = = =


Learning Goals:

I can define slope I can determine the slope and the y-

intercept of a line, given its equation. I can compare the steepness and

direction of lines given their equations I can calculate the slope of a line

from the graph

Lesson 3: The Equation of a Line



The Equation of a Line is:

y = mx + b

Where m is the slopeAnd b is the y-intercept



Identify the slope and y-intercept for each of the following:

Y = 2x – 4 y = -3x + 6 y = 9x

Y = 5 – 3x y = y = 5 – 2x

Y = -9 + y = y = -4 - x



What is Slope?

Slope is the measure of the steepness of a line.

Where do we see slopes?


Which hill is steeper?

Hill A: rises 2m over a horizontal run of 8m.

Hill B: rises 4m over a horizontal run of 10m.



We represent slope with the letter “m”.We can write slope several different ways:

m = slopem =

m =

m =

m =

Rise: The vertical distance between two points

Run: The horizontal distance between two points



You have already calculated slopes from a graph!



Success Criteria for finding the slope between two points using a graph:

Plot the pointsConnect the points with a straight lineDraw a rate triangle between the two

pointsCount up for the riseCount across for the runPut your rise and run into:Put your rise over run fraction into

lowest terms

m =



Example Success Criteria for finding the slop between two points using a graph:

Plot the points Connect the points

with a straight line Draw a rate triangle

between the two points

Count up for the rise Count across for the

run Put you rise and run

into: m = Put your fraction in

lowest terms•

•

A

B



Use the graph to calculate the slope between the points (-3, -1) and (4, 3)

Success Criteria for finding the slop between two points using a graph:

Plot the points Connect the points

with a straight line Draw a rate triangle

between the two points

Count up for the rise Count across for the

run Put you rise and run

into: m = Put your fraction in

lowest term



What do you notice about the steepness of each line segment and the speed (a.k.a. slope)



Bigger Slope = Steeper Line

Smaller Slope = Flatter Line




https://www.desmos.com/calculator/1rf9v33t86




Put the following lines in order from least steep to steepest (Direction does not matter)


Y = 2x – 4 y = -3x + 6 y = 9x

Y = 5 – 3x y = y = 5 – 2x

Y = -9 + y = y = -4 - x


What does the sign (Positive or negative) of the slope tell us?








Positive Slope = Line goes UP to the right

Negative Slope = Lines goes DOWN to the right



State if the line will go up to the right or down to the right


Y = 2x – 4 y = -3x + 6 y = 9x

Y = 5 – 3x y = y = 5 – 2x

Y = -9 + y = y = -4 - x


b in y = mx + b is the y-intercept.


The y-intercept is the point where the line crosses the y-axis.

The x-value of the y-intercept is always:

The y-intercept is also known as:






Identify the y-intercepts. The “b”


Practice

Pg. 127 #1 – 5 Pg. 128 #12

Pg. 133 #1-3, 5


Unit 5: Analytic Geometry Minds On. Unit 5: Analytic Geometry Learning Goals: I can define slope I can determine the slope and the y- intercept of.

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