Linear Equations

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 (positive or negative).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of 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

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, where there is no change in y as x changes.

Front

How can you determine if a point is a solution to a linear equation?

Back

To determine if a point (x, y) is a solution, substitute x into the equation and see if the resulting y equals the y-coordinate of the point.

Front

What is the solution to a system of linear equations?

Back

The solution to a system of linear equations is the point (or points) where the lines represented by the equations intersect.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on the Cartesian plane.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form (y = mx + b), start at the y-intercept (0, b) and use the slope (rise/run) to find another point.