M1 - Is it a Solution? (pre-systems)

Front

What is a solution to an equation?

Back

A solution to an equation is a value or set of values that makes the equation true when substituted into it.

Front

What does the ordered pair (x, y) represent in a coordinate system?

Back

The ordered pair (x, y) represents a point on the Cartesian plane, where 'x' is the horizontal coordinate and 'y' is the vertical coordinate.

Front

How do you determine if a point is a solution to an equation?

Back

To determine if a point is a solution, substitute the x-value into the equation and check if the resulting y-value matches the y-value of the point.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

What does it mean for a point to satisfy a system of equations?

Back

A point satisfies a system of equations if it makes all equations in the system true when substituted.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

How can you verify if (3, 2) is a solution to the equation y = -\frac{2}{3}x + 4?

Back

Substitute x = 3 into the equation: y = -\frac{2}{3}(3) + 4 = 2. Since the calculated y-value matches the point, (3, 2) is a solution.

Front

What is the process to check if (-3, -7) is a solution to the system of equations y = 4x + 5 and y = x - 4?

Back

Substitute x = -3 into both equations: For y = 4(-3) + 5 = -7 and y = -3 - 4 = -7. Since both equations are satisfied, (-3, -7) is a solution.

Front

What does it mean if a point is not a solution to an equation?

Back

If a point is not a solution, it means that substituting the x-value into the equation does not yield the corresponding y-value.

Front

What is the definition of a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically expressed in the form y = mx + b.