Matching Equations to tables and graphs

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 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 determine if an equation matches a table of values?

Back

To determine if an equation matches a table of values, substitute the x-values from the table into the equation and see if the resulting y-values match those in the table.

Front

What is the function of the equation y = x - 3?

Back

The function of the equation y = x - 3 is to show that for every unit increase in x, y increases by the same amount, but starts 3 units lower.

Front

What does the equation y = 10x + 5 represent?

Back

The equation y = 10x + 5 represents a linear function where for every increase of 1 in x, y increases by 10, starting from 5.

Front

What is the significance of the coefficient in front of x in a linear equation?

Back

The coefficient in front of x (the slope) indicates how much y changes for a unit change in x. A larger coefficient means a steeper slope.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if the points form a straight line.

Front

What does the equation y = 1/4x - 3 indicate about the slope?

Back

The equation y = 1/4x - 3 indicates that for every 4 units increase in x, y increases by 1 unit, showing a gentle slope.

Front

What is the relationship between the equations y = -3x + 10 and y = 3x + 16?

Back

The equations y = -3x + 10 and y = 3x + 16 represent lines with opposite slopes. The first has a negative slope, while the second has a positive slope.