Graphing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form 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 (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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).

Tags

CCSS.8.EE.B.5

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you graph a linear equation using the slope and y-intercept?

Back

To graph a linear equation, start at the y-intercept (0, b) on the y-axis, then use the slope (rise/run) to find another point on the line.

Front

What is the difference between a positive and negative slope?

Back

A positive slope means the line rises from left to right, while a negative slope means the line falls from left to right.

Tags

CCSS.8.EE.B.5

Front

What does it mean if a linear equation has a slope of 0?

Back

If a linear equation has a slope of 0, it means the line is horizontal and does not rise or fall; it represents a constant value of y.

Tags

CCSS.8.EE.B.5

Front

What does it mean if a linear equation has an undefined slope?

Back

An undefined slope occurs in a vertical line, where x remains constant and y changes; it cannot be expressed as a ratio.

Tags

CCSS.8.EE.B.5

Front

How do you determine if a point (x, y) lies on the line of a linear equation?

Back

To determine if a point (x, y) lies on the line, substitute x into the equation and see if the resulting y equals the y-coordinate of the point.