Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

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 find the slope 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 linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

What is point-slope form of a linear equation?

Back

Point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

Convert the equation 3x - 2y = -16 to slope-intercept form.

Back

The slope-intercept form is y = (3/2)x + 8.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line goes downwards from left to right.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line goes upwards from left to right.

Front

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

Back

The slope can represent rates of change in various contexts, such as speed, cost per item, or growth rates.