Writing a Linear Equation from a Table or Two Points

Front

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

Back

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

Front

How do you find the slope (m) 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 line?

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 determine the equation of a line given two points?

Back

To determine the equation of a line given two points, first calculate the slope using the slope formula, then use one of the points to solve for the y-intercept, and finally write the equation in slope-intercept form.

Front

What does it mean for a line to have a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.

Front

What does it mean for a line to have a negative slope?

Back

A line with a negative slope falls from left to right, indicating that as x increases, y decreases.

Front

How do you convert the equation of a line from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the significance of the point (0, b) in the slope-intercept form?

Back

The point (0, b) represents the y-intercept of the line, where the line crosses the y-axis.

Front

How can you verify if a point lies on a given line?

Back

To verify if a point (x, y) lies on a line represented by the equation y = mx + b, substitute the x-value into the equation and check if the resulting y-value matches the y-coordinate of the point.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.