Linear Functions

Identifying Linear Functions

100

What is a function called whose graph forms a straight line?

linear function

200

What are the two defining components of a linear function?

Rate of change (slope) and fixed value (y-intercept)

300

Tell whether the function is linear and turn it into standard form of linear equation: y=x+3

Yes can be written as 

-x+y=3

400

Tell whether the set of ordered pairs satisfies a linear function. Explain (2,4), (5,3) (8,2), (11,1)

Yes, constant change in 3 for x. Constant change of -1 in y

500

What is the cutoff for the correlation coefficient to be considered a strong correlation?

0.8 or -0.8

Using Intercepts

100

What is the x-coordinate of a y-intercept?

0

200

Find the y intercept: 2x - 4y=8

y=-2

300

Find the x and y intercepts of 3x+4y=24

x=8 and y=6

400

Find the x and y intercepts of 3x - 2y=12

x=4 and y=-6

500

Find the y intercept for the line that passes through the point (2,3) and has a slope of -4

b=11

Slope

100

What is the slope of a horizontal line?

Zero

200

What is the slope of a vertical line?

Undefined

300

Find the slope between the points (4,-2) and (-1,2)

 -4/5

400

Find the slope of the function: 6x + 5y=30

What is -6/5

500

How do you know when two lines have perpendicular slopes?

When the product of the slopes equal -1 (opposite reciprocals)

Slope intercept form

100

What is the m and what is the b in y=mx+b?

m=slope (rate of change)

b=y-intercept (initial amount)

200

Write the equation in slope intercept form: slope=-5, y intercept =0

y=-5x

300

Write the equation in slope intercept form: slope=4 and (2,5) is on the line

y=4x-3

400

Write the equation in slope intercept form: 3x+2y=8

y=-3/2x+4 

500

A caterer charges $120 to cater a party for 15 people and $200 for 25 people. Assume that the cost, y, is a linear function of the number of x people. Write an equation in slope-intercept form for this function.

y=8x

Point Slope form & standard form

100

Write the linear equation in point slope form: Slope=-7 ; (4,2)

y-2 = -7(x -4)

200

What lines have the same slope?

parallel

300

Elias has $18 to spend on peanuts and pretzels for a party. Peanuts cost $3 per pound and pretzels cost $2 per pound. Write an equation in standard form to model this scenario.

3x+2y=18

400

Write this equation in point slope form & in slope intercept form: slope=-4, (-1,-2)

Point slope form: y+2= -4(x+1) Slope intercept: y=-4x -6

500

Suppose you have $60 to buy shrimp and chicken wings for a party.  Shrimp costs $10/lb and wings cost $6/lb.

Write a linear equation that could be used to determine the number of pounds of each food that can be purchased with $60.

10s + 6w = 60