Enrichment - January 7 '25

Front

What are the x- and y- intercepts?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0). For example, in the intercepts (5,0) and (0,5), (5,0) is the x-intercept and (0,5) is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction. It is calculated as the change in y divided by the change in x (rise/run). A positive slope rises from left to right, while a negative slope falls.

Front

What slope is perpendicular to m = 3?

Back

The slope that is perpendicular to m = 3 is m = -1/3. Perpendicular slopes are negative reciprocals of each other.

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. For example, the lines y = 1/2x + 2 and y = 1/2x - 4 are parallel.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. For example, if one line has a slope of 3, a perpendicular line would have a slope of -1/3.

Front

How do you convert the equation y = mx + b to standard form?

Back

To convert y = mx + b to standard form (Ax + By = C), rearrange the equation to get all terms on one side. For example, y = 1/4x + 4 becomes x - 4y = -16.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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

Back

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

Front

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

Back

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

Front

How do you find the slope from two points?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.