Flashcardizz: Solutions to 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 (upward or downward).

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 the value of y when x = 0.

Front

How do you find the y-coordinate for a given x in the equation y = 2x + 1?

Back

Substitute the value of x into the equation and solve for y. For example, if x = 5, then y = 2(5) + 1 = 11.

Front

What ordered pair is a solution to the equation 2x + 3y = 10?

Back

To find a solution, substitute the values of x and y from the ordered pairs into the equation. For example, (5, 0) gives 2(5) + 3(0) = 10, which is true.

Front

What is the solution to the equation y = -2x + 5 when x = 2?

Back

Substituting x = 2 into the equation gives y = -2(2) + 5 = 1. So, the ordered pair (2, 1) is a solution.

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 the equation holds true, then it is a solution.

Front

What y-coordinate completes the ordered pair (0, ___) for the equation y = 2x + 1?

Back

Substituting x = 0 gives y = 2(0) + 1 = 1. So, the ordered pair is (0, 1).

Front

What is the significance of the equation y = 3x?

Back

This equation represents a linear relationship where for every unit increase in x, y increases by 3. The slope is 3 and the y-intercept is 0.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values of x and y that satisfy it. This often occurs when the lines represented by the equations are parallel.