Slope
What does the slope of a line represent?
The change in y divided by the change in x.
Define the y-intercept of a line.
The y-coordinate where the line crosses the y-axis.
Solve for x: 3x + 5 = 14.
x = 3.
How many solutions can a system of linear equations have?
One, none, or infinitely many.
How can you graph the equation y = 2x - 4?
Plot points, use slope and y-intercept, or create a table of values.
If a line has a positive slope, how will it slant on the coordinate plane?
It will slant upwards from left to right.
If a line passes through the point (0,-5), what is the y-intercept.
The y-intercept is -5.
What is the solution to the equation 2y - 7 = 3y + 2?
y = -9.
Define a consistent system of equations.
A system with at least one solution.
What does the point (3,5) represent on a graph?
A specific point with coordinates (3,5).
What is the slope of a horizontal line?
The slope of a horizontal line is 0.
How does the y-intercept appear in the equation of a line?
It appears as the constant term (b) in the equation y = mx + b.
Write the equation of a line with a slope of 2 passing through the point (1,4).
y = 2x + 2.
In a system of equations, when lines are parallel, how many solutions are there?
No solution.
How does a line look on a graph if it has a negative slope?
It slants downward from the left to the right.
If the slope of a line is undefined, what type of line is it?
A vertical line.
What is the y-intercept of a horizontal line?
The y-intercept is the y-coordinate of any point on the line.
If 4x -3 = 5, what is the value of x?
x = 2.
Solve the system of equations:
2x - y = 5
x + 3y = 7
x = 2, y = -1.
Graph the inequality: y > -2x + 3
Shaded area above the line.
Calculate the slope of a line passing through points (3,4) and (7,8).
Slope = (8 - 4) / (7-3) = 1.
Determine the y-intercept of the line with the equation y = 2x - 3.
The y-intercept is -3.
Solve the system of equations:
2x + y = 8
3x - 2y = 1
What is a necessary condition of a system of equations to have exactly one solution?
The lines must intersect at a single point.
If two lines on a graph are perpendicular, what can you say about their slope?
Their slopes are negative reciprocals of each other.