Linear equations (two variables)

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 (upward or downward).

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 find the slope from two points (x1, y1) and (x2, y2)?

Back

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

Tags

CCSS.8.EE.B.5

Front

If a linear equation is y = 3x + 2, what is the slope and y-intercept?

Back

The slope is 3 and the y-intercept is 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

A negative slope means that as x increases, y decreases. The line goes down from left to right.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

Write the equation of a line with a slope of 2 and a y-intercept of 5.

Back

The equation is y = 2x + 5.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Tags

CCSS.8.EE.B.6

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1 (m1 * m2 = -1).

Tags

CCSS.8.EE.B.6