Equations of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented 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 y-intercept of a line?

Back

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

Front

How do you determine if a graph has a positive correlation?

Back

A graph has a positive correlation if, as the x-values increase, the y-values also increase, resulting in an upward-sloping line.

Front

How do you determine if a graph has a negative correlation?

Back

A graph has a negative correlation if, as the x-values increase, the y-values decrease, resulting in a downward-sloping line.

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

Convert the equation y - 12 = -2(x - 3) to slope-intercept form.

Back

y = -2x + 18.

Front

Write the equation of a line with a slope of 2/3 and a y-intercept of 3.

Back

y = (2/3)x + 3.

Front

What is the formula to find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

How do you find the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.