Jan 9 Thurs Flashcard Functions, Slopes, Intercepts and Equations

Front

What is a function?

Back

A function is a relationship between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x). It is often represented as 'm' in the equation of a line.

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis. It is represented as 'b' in the slope-intercept form of a linear equation, which is y = mx + b.

Front

Write 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 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 does it mean if the slope is positive?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

What does it mean if the slope is negative?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a line passes through the point (1, 2) and has a slope of 3, what is the equation of the line?

Back

Using the point-slope form, the equation is y - 2 = 3(x - 1), which simplifies to y = 3x - 1.

Front

What is the slope of the line represented by the equation y = -5x + 4?

Back

The slope of the line is -5.