equation from table

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 or negative).

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you determine the equation of a line from a table of values?

Back

To determine the equation, identify the pattern in the changes of x and y values, calculate the slope (m), and use a point to find the y-intercept (b).

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

If a table shows the values (1, 3) and (2, 5), what is the slope?

Back

The slope (m) is (5 - 3) / (2 - 1) = 2.

Tags

CCSS.8.EE.B.5

Front

What is the equation of a line with a slope of 2 and a y-intercept of 1?

Back

The equation is y = 2x + 1.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you verify if a given equation matches a table of values?

Back

Substitute the x-values from the table into the equation and check if the resulting y-values match those in the table.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as x increases, y decreases, meaning the line goes downwards from left to right.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the equation y = mx + b?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept, providing a clear way to graph the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3