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.

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).

Front

What is the y-intercept?

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.

Front

What is a table of values in relation to a linear equation?

Back

A table of values lists pairs of x and y values that satisfy a linear equation, showing how y changes as x changes.

Front

What is the purpose of graphing a linear equation?

Back

Graphing a linear equation visually represents the relationship between x and y, making it easier to understand and analyze the equation.

Front

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

Back

A table satisfies an equation if every pair of x and y values in the table makes the equation true when substituted.

Front

How can you determine if a point lies on a line?

Back

To determine if a point lies on a line, substitute the x-value of the point into the equation of the line. If the resulting y-value matches the y-value of the point, it lies on the line.

Front

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

Back

The equation is y = 2x - 3.

Front

What is the relationship between the slope and the direction of a line?

Back

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