Multiple representations 7.4A, 7.7A

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 (upward or downward).

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 the value of y when x is 0.

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 is the equation of a line with a slope of -2/3 and a y-intercept of -2?

Back

The equation is y = -2/3x - 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you represent a real-world situation with a linear equation?

Back

You can represent a real-world situation by identifying the variables, determining the relationship between them, and writing an equation that models that relationship.

Tags

CCSS.8.EE.C.8C

Front

What does it mean for a table of values to satisfy an equation?

Back

A table of values satisfies an equation if, when you substitute the x-values into the equation, the corresponding y-values match those in the table.

Front

What is the relationship between a graph and its equation?

Back

The graph visually represents the solutions of the equation. Each point on the graph corresponds to an (x, y) pair that satisfies the equation.

Front

How do you interpret the meaning of the coefficients in a linear equation?

Back

The coefficients represent the rate of change and the starting value in a real-world context. For example, in y = mx + b, m is the rate of change and b is the starting value.

Tags

CCSS.HSF.LE.B.5

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value). It can be represented by an equation, a table, or a graph.

Tags

CCSS.8.F.A.1