Linear Systems 1

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 it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect, meaning they have no solution when represented as a system of equations.

Front

What does it mean for two lines to coincide?

Back

Two lines coincide if they lie on top of each other, meaning they have infinitely many solutions as every point on the line is a solution.

Front

How do you find the slope of a line from an equation?

Back

To find the slope of a line from an equation in the form y = mx + b, identify the coefficient m, which represents the slope.

Front

What is the y-intercept of a linear equation?

Back

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

Front

Solve the system of equations: y = x - 1 and -x + y = 2.

Back

The lines are parallel, so there is no solution.

Front

Solve the system of equations: 4y - 5x = 9 and x - 4y = 11.

Back

The solution is (-5, -4).

Front

Solve the system of equations: y = 2x - 1 and y = -x + 5.

Back

The solution is (2, 3).

Front

What is the slope of the equation y = -3x + 4?

Back

The slope is -3.

Front

Identify the y-intercept for the function y = -3x.

Back

The y-intercept is 0.