Where the Slope at?
What is the slope of the line that passes through the points (- 8, -2) and (17, - 4).
- 4 - (-2 ) -2
__________ = ___
17 - (-8) 25
A line has an undefined slope and passes through the point (85, -74). Write the equation of the line.
x = 85
Explain:
1.) What makes a slope undefined?
2.) What make a slope zero?
Answers may vary:
1.) creates a vertical line, all of the x's are the same, the equation is " x = ____" , hits the x-axis
2.) Creates a horizontal line, all the y's are the same, the equation is " y= ___" , hits the y-axis
Find the x and y intercepts of the line given by
-15x - 12y = 75
x- intercept = 75/ -15 = -5
y-intercept= 75 / -12= - 6.25
A line passes through the point (20, -5) and has a slope of - 3/4.
Write the equation of this line in point-slope form.
y + 5 = -3/4 (x - 20)
Amy found a style of ducks that she loves online. She has to pay for each duck plus a fixed shipping cost. She has 6 ducks in her cart right now and her total cost is $22.69 (including shipping). Later she decides to add 4 more ducks to her cart. Her total is now $32.49 (including shipping).
What is the cost of each duck?
32.49 - 22.69 = 9.80
10 - 6 4
$ 2.45 Per duck
Graph the equation
y = -2/5x + 3
Graph details
- m =-2/5 (goes down 2, right 5)
- hits the y axis at (0,3)
- Line is decreases from left to right
Bailey borrowed money from her mom to get her car fixed and pays her back with weekly payments. The table shows the amount, A, she still needs to pay back, in dollars, and the number of weeks, w, since she borrowed the money.
Weeks (w) l 1 l 2 l 3 l 5 l
Amount ($) l 455 l 390 l 325 l 195
1.) About many weeks will it take her to pay her mom back?
m = -65 ; b = 520
520/ 65 = 8 weeks
It will take her 8 weeks to pay her mom back
Find the x and y intercepts of the line given
25 x - 18 y = -140
x intercept = -140 / 25 = -5.6
y-intercept = -140 /-18 = 7.77
A line passes through the point (-18, -12) and has a slope of 13. Write the equation of this line in point-slope form.
y + 12 = 13 (x + 18)
Amy found a style of ducks that she loves online. She has to pay for each duck plus a fixed shipping cost. She has 6 ducks in her cart right now and her total cost is $22.69 (including shipping). Later she decides to add 4 more ducks to her cart. Her total is now $32.49 (including shipping).
What is the Shipping cost?
m = 2.45 per duck
22.69 = 2.45(6) + b
22.69 = 14.70 + b
- 14.70 - 14.70
7.99 = b ; Shipping is $7.99
Write the equation of the linear function given by the table below.
x l -4 l 0 l 4 l 8 l 10
y l 46 l 38 l 30 l 22 l 14
m = y /x = -8/4 = -2/1
** We can find b by looking for a "0" in the x **
b = 38 & m = 1/2
y = -2 x + 38
15 boxes of pencils weigh 10 pounds.
How much would 8 boxes weigh?
How many boxes are there if the weight is 24 pounds?
1.)
15 boxes = x boxes
10 pounds 8 pounds
15* 8 = 10*x
120 = 10x
10 10
x = 12 boxes
2.)
15 boxes = x boxes
10 pounds 24pounds
10* x = 24*15
10x = 360
10 10
x= 36 pounds
At PetSmart, fish cost $8 and the plants for the fish cost $12. Samantha has $125 to spend.
Write an equation that models the possible combinations of fish, f, and plants, p Samantha can buy.
8f + 12p = 125
or
8x + 12y = 125
Graph the point-slope equation
y + 1 = 2 ( x - 4)
Graph details
- m = 2/ 1 (goes up 2, right 1)
- point ( 4, -1)
- Line is increasing from left to right
Write the equation in slope-intercept form
(1, −19) & (−2, −7)
1.) Find slope
-7 - (-19) = 12 = -4
-2 - 1 -3
2.) choose a point to plug into y=mx+b & find b
( 1, -19 ) & m = 2
y = m * x + b
-19 = -4 * (1) + b
-19 = -4 + b
+4 +4
-15 = b
Equation: y = -4x-15
Write an equation with a slope of -5 and goes through the point ( -2 , 15) .
y = m x + b
15 = -5 * (-2) + b
15 = 10 + b
-10 -10
5 = b
y= -5x + 5
A line with an undefined slope passes through the point (-4,-11), and (k, j). Find the value of k.
k = - 4
** For undefined lines, all of the x-values are the same **
A bag of dog food weighs 25 pound and a bag of cat food weighs 12 pound. Bill can only carry 75 pounds because of a sports injury.
Write an equation that models the possible combinations of pounds of dog food , d , and pounds of cat food , c , Bill could carry.
25d + 12c = 75
or
25x + 12y = 75
Graph the point slope formula
y + 5 = -2/3 ( x + 3)
Graph details
- m = -2/3 (goes down 2, right 3)
- point ( -3, -5)
- Line is decreasing from left to right