Writing Linear Equations from Tables

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 slope means the line rises, negative slope means it falls).

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the slope from a table of values?

Back

To find the slope from a table, calculate the change in y (rise) divided by the change in x (run) between two points: m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

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

Back

The equation is y = 2x + 3.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you write the equation of a line from a table?

Back

Identify two points from the table, calculate the slope using those points, and then use one point to find the y-intercept to write the equation in the form y = mx + b.

Front

What is the equation of a line that passes through the points (1, 6) and (3, 10)?

Back

First, find the slope: m = (10 - 6) / (3 - 1) = 2. Then use point (1, 6) to find the y-intercept: 6 = 2(1) + b, so b = 4. The equation is y = 2x + 4.

Front

What does it mean if a linear equation has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that the value of y does not change as x changes.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = -3x + 5?

Back

The slope of the line is -3.

Tags

CCSS.8.EE.B.5

Front

How do you convert the equation y = 1/2x + 2 into slope-intercept form?

Back

The equation is already in slope-intercept form, where the slope is 1/2 and the y-intercept is 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3