3.5, 3.6, and 4.2 Flashcard Review

Front

What is the definition of slope in a linear equation?

Back

The slope (m) of a line is a measure of its steepness, calculated as the change in y divided by the change in x (m = Δy/Δx).

Front

How do you find the slope of a line given two points?

Back

To find the slope of a line given two points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean if the slope of a line is undefined?

Back

An undefined slope occurs when a line is vertical, meaning the x-coordinates of the two points are the same, resulting in division by zero.

Front

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

Back

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

Front

How do you write the equation of a line in slope-intercept form?

Back

To write the equation of a line in slope-intercept form, identify the slope (m) and the y-intercept (b) from a point on the line or from two points.

Front

What is an x-intercept?

Back

The x-intercept is the point where a line crosses the x-axis, which occurs when y = 0.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept of a linear equation, set y = 0 and solve for x.

Front

What is the significance of the slope in a table of values?

Back

The slope in a table of values indicates the rate of change between the dependent and independent variables.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form, start at the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.