Forms of linear equations
The equation x/1 + y/-4 = 1 is in intercept form.
What are the coordinates of the y-intercept?
(0, -4)
What is the midpoint of the two points (0, 0) and (5, -6)?
The line y = 3x + 1 passes through the point (10, 31). If y represents the amount of money in my wallet after x days, interpret the point given using words.
After 10 days, I have 31 dollars in my wallet
In the line y = x + 2, what is the slope?
1
How old am I? (I am in 20th grade)
25
The equation (y - 5) / (x + 3) = 4 is in point-slope form.
Name a point on this line.
Answers may vary. (5, -3)
A line segment has endpoints of (4, -13) and (10, 17)
What are the coordinates of this segment's midpoint?
(7, 2)
Give a point on the line and explain what it means in the context of the problem.
Answers vary
(0, 100) 0 hours since full charge, the phone is at 100%
(1, 92) 1 hour since full charge, the phone is at 92%
Line AB is parallel to line CD. Line CD has a slope of -5.
What is the slope of line AB?
-5
What school did I teach at before coming here?
Stemmers run middle school (in essex)
The equation 2x + 3y = 6 is in general form.
Name a point on this line.
Answers vary. Plug in a value for x or y and solve for the other
What is the distance between (0, 0) and (3, 4)?
5
My water bottle has a leak in it :(
Assuming water flows out linearly according to the equation y = -2.5x + 32, the bottle will have y = 9.5 ounces remaining after how many hours?
x = 9 hours
If a line has a slope of -3, what is the slope of a line perpendicular to that one?
1/3
What is my favorite color?
Orange
A line passes through the points (0, 4) and (-5, 24).
Write any equation for a line that passes through these points.
Answers vary.
y = -4x + 4
4x + y = 4
x + y/4 = 1
(y - 4)/x = -4
(y - 24)/(x + 5) = -4
What is the distance between (5, 7) and (-1, 9)?
sqrt(40) = 2sqrt(10)
The equation to convert from Fahrenheit to Celsius is F = 9C/5 + 32
If it is 77 degrees Fahrenheit out, what temperature would that be expressed as in Britian (and most of the rest of the world)?
25 C because 77 - 32 = 45. Then multiply by 5/9.
Line PQ is parallel to line XY. XY passes through the points (-1, 10) and (3, 18)
What is the slope of line PQ?
2
What is the solution to the following system of equations? Solve algebraically or graphically.
5x + y = 20
2x - y = 1
(3, 5)
Add the two equations to get 7x = 21, so x = 3. Then solve for y = 5. Or just graph it.
Write this equation in two of the three other forms we have learned.
Answers may vary.
3x + y = -6 is standard form
x/-2 + y/-6 = 1 is intercept form
(y + 6)/x = -3 is an example of point-slope form
If two points are located at (2, 7) and (-3, -5), what is the distance to the midpoint between them?
6.5 because sqrt(5^2 + 12^2) = sqrt(169) = 13
13/2 = 6.5
If I drop an object from a plane, its velocity can be found by the equation v = 9.8t
If t = seconds and v = velocity in meters/second, Interpret the slope of this line using words.
The velocity of a falling object will increase 9.8 meters/second every 1 second due to gravity (which we call gravitational acceleration)
Line FG is perpendicular to line HI. Line HI passes through the points (-6, 11) and (4, 31)
What is the slope of line FG?
-1/2
21 because...
0, 1, 2, 3, 4, 5, 6
10, 11, 12, 13, 14, 15, 16
20, 21