Graphing Linear Equations

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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 as (0, b) in the slope-intercept form y = mx + b.

Front

How can you determine the y-intercept from the equation of a line?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.

Front

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

Back

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

Front

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

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to isolate it on one side of the equation.

Front

What is the first step to solve for slope-intercept form in the equation -x + 4y = 11?

Back

Add x to both sides to isolate the term with y.

Front

What does the term 'standard form' refer to in linear equations?

Back

Standard form refers to the format Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you identify the slope from a graph of a linear equation?

Back

The slope can be identified by selecting two points on the line and calculating the rise over run between them.

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change, which can indicate how one variable changes in relation to another in real-world scenarios.