7.7A 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 of a line represent?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the slope from 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 does it mean if a line has a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.

Tags

CCSS.8.EE.B.5

Front

What does it mean if a line has a negative slope?

Back

A line with a negative slope falls from left to right, indicating that as x increases, y decreases.

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 determine if a point lies on a line represented by a linear equation?

Back

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

Front

What is the difference between a function and a non-function in terms of linear equations?

Back

A function has only one output (y) for each input (x). A non-function may have multiple outputs for a single input, which is not allowed in linear equations.

Tags

CCSS.8.F.A.1

Front

What is a real-world example of a linear equation?

Back

An example of a linear equation in the real world is a phone plan that charges a fixed monthly fee plus a variable cost per minute used.

Tags

CCSS.8.EE.C.7B