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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.6

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.