Linear Equations And Their Graphs Flashcards
How do you know that the equation y = x is a linear equation?
If an equation contains an x and/or a y variable, neither of which has an exponent greater than one, it is a linear equation.
What does the graph of a linear equation look like?
A linear equation creates a line when graphed on a coordinate plane.
Is y = 5 a linear equation?
Why or why not?
An equation is “linear” if it contains a an x and/or a y variable that do not contain an exponent greater than 1.
Which of these equations are linear?
y = 4 x = 2 y = x - 1
Why did you choose the equation (s) ?
All three are linear equations. All three equations contain an x and/or a y variable that are not raised to any power greater than one.
What is the name of this form of equation?
y = mx + b
Slope Intercept Form
What is the name of an equation in this form ?
ax + by = c
Standard Form
In this equation, the 2 is the slope, m. What is another name used to describe this number in front of the x variable?
y = 2x + 5
the coefficient of x
In the equation y = 3x + 5, 5 is the y intercept, b. What is another word used to describe the 5 in this equation ?
the constant
What is true about the lines that represent these two equations?
y = 4x - 3
y = 4x + 1
The lines are parallel, because they have the same slope.
What is true about the lines that represent this system of equations?
y = -2x + 1
y = 3x
The lines will intersect and create exactly one solution, because the lines have different slopes.
If the constant is changed in the linear equation, y = x - 4 from -4 to 6, describe what would happen to the graphed line ?
The line would shift up on the y axis.
How many units on the y axis would a line move if the y intercept is changed from a -2 to a 5 ?
The line would move up 7 units on the y axis.
What happens to the line that represents the equation y = -2x + 5 if the coefficient of x is changed to a 4?
The line gets steeper.
What happens to the line that represents the equation y = 1/2x - 5, if the coefficient of x is changed to 1/8 ?
The line will become less steep.
What causes a system of equations to have “no solution”?
The equations have the same slopes, which means the lines are parallel.
What is true of a system of equations that has “infinite solutions”?
The equations are the same.
If a system of equations has a solution, how is that solution written?
A solution to a system is written as an “Ordered Pair”.
What is the slope in the equation y = -x + 4 ?
The slope is -1.
What is the y intercept of the equation y = -3/4x + 2 ?
The y intercept is 2.
What “type of slope” is one that runs uphill from left to right on the graph?
Positive slope
What “type of slope” runs downhill from left to right on the graph?
A negative slope.
What “type of slope” is a line that runs across the graph horizontally?
Zero slope
What “type of slope” is a line that runs vertically on the graph ?
Undefined or No Slope
