Linear Relationships
What are the two most common variables for linear equations?
x and y
It has an inequality sign (>, <,≥,≤).
Two or more linear equations in the same variable form are ___________________.
a system of linear equations
__________ is equal to the ratio of a line's change in y-value to its change in x-value.
Slope
Horizontal lines have a slope of _____.
0
What is slope-intercept form of a linear function?
y=mx+b
Solve: -3p-7<p+9
p>-4
Solve the systems of equation using the substitution method. Make sure your answer is in a solution set (x,y).
x=y-4
2y=x+7
(-1,3)
2. This is when y=0
1. y-intercept (0,__)
2. x-intercept (__,0)
Which symbol has a graph with an open circle?
> <
Tamika purchases a new mattress for $600, which she will pay for with an initial payment of $150 and monthly installments of $30. Which equation can be used to find the number of monthly installments, m, required to complete the purchase, assuming there are no taxes or fees?
600=30m+150
Which of the following numbers is NOT a solution to the inequality: 7x-3≤3x+11
a. 3
b. 0
c. 4
d. 3.4
x≤3.5
c. 4
D A I L Y D O U B L E
Name the 3 ways to solve systems of linear equations.
1. Graphing
2. Elimination
3. Substitution
The ________ the line is, the __________ the magnitude of its slope is.
Steeper
Larger
3x-4y=12
Slope (m) =______
Y-intercept (b)=______
Slope (m) =3/4
Y-intercept (b)= -3 or (0,-3)
Find the equation of a line passing through (-4,-7) and (-6,9). Express the equation in slope-intercept form.
y=-8x-39
Solve: 8(1-2x)<32
x> -3/2
What method should be used to solve the following system of equations? What is the solution (x,y)?
-3x+7y= -16
-9x+5y= 16
1. Elimination
2. (-4,-4)
Convert the following equation into slope-intercept form and tell me what the y-intercept is.
4x+2y=-8
y=-2x-4
(0,-4)
Give three ways/formulas that slope can be written.
increase in vertical/increase in horizontal
change in y/change in x
∆y/∆x
m=y2-y1/x2-x1
3x+4y=12
1. What form is this in?
2. What is the slope (m)?
3. What is the y-intercept (b)?
1. Standard
2. -3/4
3. 3
│5-3x│> 8
x<-1 AND x<13/3
What is the solution (x,y) to the system of linear equations?
5x+3y=2
3x+5y=-2
(1,-1)
Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
(-3, 14) and (1,-2)
(0,-3) and (-2,5)
Both lines have a slope of -4, so these lines are Parallel
D A I L Y D O U B L E
Name the 4 Khan Academy lessons we have covered so far.
1. Understanding Linear Relationships
2. Solving Linear Equations and Linear Inequalities
3. Solving Systems of Linear Equations
4. Graphing Linear Equations