Slope/SI-Form
Find the slope between these points:
(-5, 6) and (-2, 3)
m = -1
Label each equation below as either Direct Variation, Vertical, or Horizontal:
1.) y = 4
2.) x = 4
3.) y = 4x
1.) Horizontal
2.) Vertical
3.) Direct Variation
What is the general form of Standard Form?
Ax + By = C
Solve the following equation for k.
y = kx
k = y/x
Find the equation of the line that has a slope of 2/3 and passes through the point (6, -5).
y = 2/3x - 9
Find the slope of each line below:
1.) y = 6
2.) x = 7
1.) m = 0 (Horizontal)
2.) m = undefined (Vertical)
What are the x- and y-intercepts of the equation below?
2x - 3y = 18
x-intercept: (9, 0)
y-intercept: (0, -6)
Solve the following equation for m.
y = mx + b
m = (y - b)/x
Find the equation of the line that passes through the points (9, -1) and (10, 2).
y = 3x - 28
Toby has 5 Labubu dolls but wants to start collecting more. So, starting next month, he plans to buy 2 dolls every month.
Is this an example of Direct Variation? Why or why not?
No, it is not Direct Variation, because he started with 5 dolls (there is a y-intercept).
Stavros has $52 to spend on Halloween candy. Sour Patch Kids are $2/lb and Reese's Peanut Butter Cups are $4/lb. Write an equation in Standard Form that models this situation.
2x + 4y = 52
Solve the following equation for w.
f = (wh)/s
w = (fs)/h
Wongo opened a savings account at the bank. He deposited money in the account when he opened it. Then, he will withdraw money from it every week to pay for gas. The equation below represents this situation:
f(x) = -20x + 500
What do the slope AND y-intercept represent in context of this situation?
slope: Wongo withdraws $20/week
y-intercept: Wongo deposited $500 when he opened the account.
Brent's pay varies directly with how many hours he works. After working 5 hours, he earned $90. After working 11 hours, he earned $198.
What is the constant of variation k in this situation AND what does it represent?
k = 18
Brent makes $18/hour
Sarah has $60 to spend on pens and keychains. The equation 1.5x + 3y = 60, where x represents how many pens she can buy and y represents how many keychains she can buy, models this situation.
Can she afford to buy 12 pens and 18 keychains?
No, should would be $12 overbudget.
12 pens = $18
18 keychains = $54
$18 + $54 = $72
What would the equation 3x - 5y = 45 be in Slope-Intercept Form?
y = (3/5)x - 9
The height (in inches) of a tree over time (in months) is modeled by the following function:
h(t) = 3x + 18
If the tree is 10.5 feet, how many years has it been growing for?
3 years
If you have 2 horizontal lines, will they ever intersect? If so, how?
Yes, if the 2 lines have the same equation!
If we were to graph Stavros' candy line (2x + 4y = 52), What would be the slope of it?
m = -1/2
Solve the following equation for b.
a2 + b2 = c2
b = sqrt(c2 - a2)