Equations of Linear Functions (Graphing and Writing Equations)

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, defined by the equation 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-coordinate with respect to the x-coordinate, indicating how steep the line is.

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 of a line given two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is an undefined slope?

Back

An undefined slope occurs in a vertical line where the change in x is zero, making the slope calculation (rise/run) impossible.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of two perpendicular lines are negative reciprocals of each other, meaning if one line has a slope of m, the other will have a slope of -1/m.

Front

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

Back

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

Front

What is the x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, found by setting y = 0 in the equation and solving for x.

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 m is the slope and (x1, y1) is a point on the line.

Front

How do you graph a linear function?

Back

To graph a linear function, identify the y-intercept (b), use the slope (m) to find another point, and draw a straight line through these points.