Linear Equations and Graphs

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you solve the equation 3(x+2) = 15?

Back

To solve, first distribute: 3x + 6 = 15. Then, subtract 6 from both sides: 3x = 9. Finally, divide by 3: x = 3.

Front

What is the solution to the equation -4x - 14 = 6?

Back

To solve, first add 14 to both sides: -4x = 20. Then, divide by -4: x = -5.

Front

What are the four quadrants in a coordinate plane?

Back

The four quadrants are: I (x > 0, y > 0), II (x < 0, y > 0), III (x < 0, y < 0), IV (x > 0, y < 0).

Front

How do you identify the quadrant of the point (10, -5)?

Back

Since x = 10 (positive) and y = -5 (negative), the point (10, -5) is located in Quadrant IV.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.