Simplify

1.                 1 + 5 + 36 – 30 + 5 = 17

2.                               5 + 36 – 30 + 5 = 16

 

Evaluate for

  1.  = ____    9 + 6 = 15
  2.                      24

Evaluate for

  1.  = ____   25 + -9 = 16
  2. = ____    9 + -21 = -12

Choose from: slope-intercept, standard, point-slope

  1. Ax + By = C is called the ____standard_______ form of the equation of a line.
  2. y = mx+b is called the ____slope-intercept________ form of the equation of a line.
  3. y-y1 = m(x-x1) is called the ___point-slope________ form of the equation of a line.

 

Fill in the blank to make a true statement.

  1. Every point on a line is a solution that line’s ___equation_____.
  2. The rate of rise to run is called the ___slope_________  of the line.
  3. The point where the line crosses the y-axis has an x-value of __ 0 ______
  4. The point where the line crosses the x-axis has a y-value of ____ 0 ____
  5. In a coordinate plane, lines are parallel if they have the same __slope _____ but different intercepts.
  6. The point where the line crosses the y-axis has an x-value of ____ 0 ____
  7. A line with a equation in the form y = b is ____horizontal____ (horizontal / vertical)
  8. A line with a equation in the form x = c is ___vertical_____ (horizontal / vertical)
  9. Lines that rise from left to right have a ___positive_______ slope.
  10. Lines that fall from left to right have a _____negative_______ slope.

 

Solve for the given variable
  1.    2x – x – 4 = x – x + 8 and x – 4 = 8 so x = 12
  2.                  4x – 4x – 1 = 5x – 4x so -1 = x
  3.                -7y + 7y + 14 = 0 + 7y and 14 = 7y so y = 2
  4.        7y = 5y + 10 and 7y – 5y = 5y – 5y + 10 and 2y = 10 so y = 5

Give the slope and y-intercept of each line:

 

  1. slope: __ 2___
  2. y-int: __ -3___

  1. slope: __m = ___
  2. y-int: __(0,0)___

 

  1. slope: __ 1 ___
  2. y-int: __(0,0)___

 

  1. slope: __ -1 ___
  2. y-int: __(0,0)___

 

Determine whether the relationship is linear, quadratic, absolute value, or circle.

32.                       quadratic: the graph of a quadratic function is a parabola

33.                               linear: the graph of a linear function is a line

34.                            absolute value

35.                               linear

36.                             circle

 

Write the equation in slope-intercept form of the line with the given slope and through the given point.                 y = mx + b

 
  1. m = 2 and through (0 . 0)                      y = 2x
  2. m = -3 and through (2 , 3)                    y = -3 + b where x=2 and y=3 so 3 = -3*2 + b so b is -3 and the equation is y = -3x - 3
  3. m = 1 and through (8, 8)    y = x + b where x =  8 and y = 8 so 8 = 8 + b and b = 0, so the equation is y = x
  4. m = -5 and through (-4 , 2)   y = x + b where x = -4 and y = 2 so 2 = -5(-4) + b, and b = -18 so the equation is y = -5x - 18
  5. m = 0 and through (8, -3)  when the slope is 0, the line is horizontal and in the form y = b so the equation is y = -3

 

Write the equation in point-slope form of the line through the two points.

y - y1 = m(x - x1)

 
  1. (6 , 2) and (0 , 0)          m =  so pick one of the points:  y – 2 = (1/3) (x – 6) or y = (1/3)x
  2. (3 ,  -2) and ( 0 , 1)      m =  so y + 2 = -1(x-3) or y – 1 = -1(x)
  3. (2 , 6) and (1 , 1)          m = so y – 6 = 5(x - 2) or y – 1 = 5(x – 1)
  4. (4 , 4)  and (7 , 7)         m =  so y – 7 = x - 7 or y - 4 = y - 4
  5. (1 , -3) and (4 , 6)        m =  so y – 6 = 3(x – 4) or y + 3 = 3(x – 1)
  6. Find the area of a rectangle with length 6 ft and width 5.5 ft.      ___A = l * w = 6 * 5.5 = 33 ft2 ___
  7. Find the area of a triangle with base 20 m and height 7 m.          ___A = 0.5 * b * h = 0.5 * 20 * 7 = 70 m2_________
  8. Given  find the equation when the time is t sec. and the rate is 35 ft/sec. ________ d = 35t 
  9.  find the equation when the time is t sec. and the rate is 60 mph._____  d = 60t 

 

  1. If a runner begins with a30 ft lead and runs 4 ft/sec faster than his opponent, how long will it take for the runner to have a 60 ft lead?         ___ to catch up 30 ft at 4 ft/sec, it will take 7.5 sec __________
  2. Where do the lines and intersect?  ____ (0 , 0) look at the y-int
  3. Where do the lines and intersect?  (  ,   ) (0 , 5)  look at the y-int
  4. Find the point of intersection for  and       (    ,    )   (-7, -1)

substitute to get x + 6 = -x – 8 and 2x = -14 so x = -7, then substitute to get y = -1

If you do this by linear combination method, it works easily  and then substitute -1 = x + 6 so x = -7

 

 

 

  1. Find the point of intersection for  and   (    ,    )  (-1, 6)

substitute to get 2x + 8 = -2x + 4 and 4x = -4 so x = -1, then substitute to get y = 6

If you do this by linear combination method, it works easily  and then solve for x:  6=2x+8 and -2 = 2x so x = -1

  1. Find the point of intersection for  and                  (    ,    )  (0, 0)

Use x = -3y to substitute 3(-3y) + y = 0 so -8y = 0 and y = 0 and x = 0.  But in the form Ax + By = C you can see that when C = 0 then the line goes through (0,0)

 

  1. A car rental company charges $45 per day plus $0.25 per mile.   Another company charges $62 per day plus $0.20 cents per mile.  If you rent for the same number of days, at what mileage are the two plans equal?            __________

Let C = cost and m = # of miles

C = 0.25m + 45   and   C = 0.2m + 62

You can substitute and get 0.25m + 45 = 0.2m +62

0.05m = 17 and divide both sides by 0.05 (or multiply by 20) to get 340.

At 340 miles, 45 + 0.25 * 340 = 45 + 85 = 130 and 62 + 0.2 * 340 = 62 + 68 = 130