Flashcardizz: Solutions to Linear Equations

Front

What is a solution to a linear equation?

Back

A solution to a linear equation is an ordered pair (x, y) that makes the equation true when substituted for x and y.

Front

How do you determine if an ordered pair is a solution to a linear equation?

Back

Substitute the x and y values of the ordered pair into the equation. If both sides of the equation are equal, then it is a solution.

Front

What is the equation of a line in slope-intercept form?

Back

The slope-intercept form of a line is 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 represents the rate of change of y with respect to x; it indicates how steep the line is.

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 y when x = 0.

Front

How can you find the y-coordinate for a given x-coordinate in a linear equation?

Back

Substitute the x-coordinate into the equation and solve for y.

Front

What is the significance of the ordered pair (0, b) in a linear equation?

Back

The ordered pair (0, b) represents the y-intercept of the line.

Front

What does it mean if an ordered pair does not satisfy a linear equation?

Back

It means that when the x and y values are substituted into the equation, the equation does not hold true.

Front

How do you check if (2, 0) is a solution to 2x + y = 4?

Back

Substitute x = 2 and y = 0 into the equation: 2(2) + 0 = 4, which is true.

Front

What is the solution to the equation y = 2x + 1 when x = 0?

Back

When x = 0, y = 2(0) + 1 = 1, so the ordered pair is (0, 1).