Determining Slopeand y-intercept

8.EE.6

Essential Question?How can you determine the slope and y-intercept of a line?

Common Core Standard:8.EE.6 ─ Understand the connections between proportional relationships, lines, and linear equations.Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Objectives:

• To determine the slope and y-intercept of a linear equation, given a graph, a table, or an equation.

Curriculum Vocabulary

Linear Equation (ecuación lineal):An equation whose solutions form a straight line on a coordinate plane.

Slope Intercept Form (forma de pendiente-intersección):A linear equation written in the form y = mx+b, wherem represents the slope and b represents the y-intercept.

y-intercept (intersección con el eje y):The y-coordinate of the point where the graph of a function crosses the y-axis.

Determining Slope and y-intercept

The following graph represents the amount of water in a water tank over a 4 week period, during a drought.

(no water is being added to the tank)

Given a GRAPH:

What is the initial value(y-intercept)?

What is the slope?

How would you interpret the slope and y-intercept in the context of the problem?

Number of weeks

Nu

mbe

r of

Gal

lon

s of

Wat

er in

Tan

k

0 1 2 3 4

1000

900

800

700

600

500

400

300

200

100

Determining Slope and y-intercept

The following equation represents the amount of money earned by a car salesperson based on the number of cars they sell each month.

Given an EQUATION :

What is the initial value(y-intercept)?

What is the slope?

How would you interpret the slope and y-intercept in the context of the problem?

Determining Slope and y-intercept

The following table represents the rate at which the Ebola virus is spreading in Africa for the month of September 2014.

Given a TABLE:

What is the initial value(y-intercept)?

What is the slope?

How would you interpret the slope and y-intercept in the context of the problem?

Number of days 6 12 18 24 30

Number of Infected 150 180 210 240 270

COMPARING LINEAR RELATIONS

Alyssa wants to take dance lessons. The table below shows the cost for group lessons and private lessons. Which is more expensive? What is the difference between the two? If Alyssa’s parents are willing to pay for the less expensive choice, how much would Alyssa need to spend if she wanted the more expensive choice?

Lessons 1 5 8 10 20

Group ($) 60 180 270 330 630

Private ($) 35 175 280 350 700

Are these both proportional? What kind of statements can you make about this situation?