Algebra 1 Slope Intercept, Direct Variation STUDY GUIDE

Algebra 1 Slope Intercept, Direct Variation Test STUDY GUIDE

Name: ___________________________________________ Date: _________________ Block: _________ Algebra 1 Slope Intercept, Direct Variation STUDY GUIDE SOLs: A.6, A.8 Find slope and rate of change

change in y

y 2  y1 Δy = x 2  x1 Δx



Slope is defined as: slope = m =



Positive slopes increase (rise) as x increases.



Negative slopes decrease (fall) as x increases.



Horizontal lines (y = a) have a slope of 0.



Vertical lines (x = a) have an undefined slope.



Rate of change compares quantities in the same way slope does.

change in x

=

Slope-Intercept Form 

Slope –intercept form for linear equations is y = mx + b, where m is slope and b is the yintercept.



Graph linear equations by: o Putting linear equation in slope-intercept form (solve for y). o Graph the y-intercept (b). o Use the slope to go up or down the change in y (numerator of slope) and left or right the change in x (denominator of slope) to find other points. o Connect points.

Direct Variation 

Direct variation equations are of the form y = kx, where k is the constant of variation.



Since the constant of variation, k, is the same for any x,y pair, find k by dividing y by y x, or k = . x Identify direct variation equations by:



o Putting equation in slope-intercept form. o If b = 0, then the equation is a direct variation. 

Direct variations are graphed in the same way as any other linear equation.

Algebra 1 Slope Intercept, Direct Variation Test STUDY GUIDE Page 2

Study Questions 1) Find the slope of the line that passes through the points. a) (2, -3) and (-1, 1)

b) (-1, -3) and (4, -3)

c) (2, 5) and (2, -6)

d) (0, 1) and (-3, 5)

e) (-3, 4) and (-5, 8)

f) (-3, 3) and (-6, 0)

2) Could any of the lines described in the previous problem be parallel? Explain your reasoning.

3) Find the slopes and y-intercepts of the lines below: a) y = -3x - 6

b) 2x + 8y = 16

c) 12x – 4y = 16

4) Graph the functions using the slope-intercept method. Remember to put the equation into slope-intercept form if necessary. Identify the slope and the y-intercept. a) y = x – 5 slope____________ y-intercept_________

c) y – 3x = 4 slope____________ y-intercept_________

b) y = -

1 x 2

slope____________ y-intercept_________

d) 4x + 2y = 12

slope____________ y-intercept_________

Algebra 1 Slope Intercept, Direct Variation Test STUDY GUIDE Page 3

5) Identify the slope of the lines shown: a)

b)

c)

d)

e)

f)

6) At the beginning of the day, you had 10 gallons of gas in the car. After driving for 4 hours, you had 2 gallons of gas in the car. What was the rate of change? 7) Which equations below show direct variation? If an equation does show direct variation, what is the constant of variation? a) y = -

2 x 3

b) 2x – 4y = 0

c) 9x + 10y = 3

d) -3x – y = 0

8) Given the y varies directly with x, write a direct variation equation that relates x and y. 1 a) x = -10, y = 5 b) x = , y = 2 c) x = -3, y = 12 d) x = 6, y =-2 3 9) Which of the graphs below show direct variation? There may be more than one. a)

b)

c)

d)

Algebra 1 Slope Intercept, Direct Variation Test STUDY GUIDE Page 4

10) Which of the tables below show direct variation? If so, what is the direct variation equation. There may be more than one table that shows direct variation. a)

b)

11) One variable (A) varies directly as the other (C). Find the missing numbers x and y. Write the formula which relates the variables.

12) There are about 200 calories in 50 grams of Swiss cheese. Willie ate 70 grams of this cheese. About how many calories were in the cheese that he ate if the number of calories varies directly as the weight of the cheese.

13) The resistance (R) of a copper wire varies directly as its length (L). Write this relation as a direct variation using k as the constant of variation.

14) The distance an object, a, drops from rest in freefall varies directly with the square of the time, t. If a varies directly as t2, and a = 12 when t = 2, find a when t = 3.

15) Graph the equations. What are the slopes of the lines? a) y = 4 slope ________

b) x = -3 slope _______

Algebra 1 Slope Intercept, Direct Variation Test STUDY GUIDE Page 5

Study Guide Answers 1) a) 

4 4 b) 0 c) undefined d)  e) -2 f) 1 3 3

2) The lines in a) and d) could be parallel because they have the same slope. 3) a) m=-3, b=-6 b) m = 

1 , b=2 c) m=3, b=-4 4

4) a) slope = 1, y-int =-5

9) a) and d) are direct variations 10) a) not direct variation b) yes, N = 2M 11) y=6, x = 5 equation: C = 3A 12) 280 calories 13) R = kL

b) slope = -

14) a = 27 when t = 3

1 , y-int = 0 2

c) slope = 3, y-int = 4 (rewrite as y = 3x+4)

d) slope = -2, y-int=6 (rewrite as y=2x+6)

5) a) m=-2 d) m=-1

b) m=0

5 e) m=2

c) m=undefined f) m=

2 3

6) -2 gal/hour (take slope of points (0, 10) and (4, 2))

2 1 b) yes; k= c) no d) yes; k=-3 3 2 1 1 8) a) y=- x b) y = 6x c) y = -4x d) y = - x 2 3 7) a) yes; k = 

15a) m = 0

15b) undefined slope