Linear Equations

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

Tags

CCSS.8.EE.B.5

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

What is the y-intercept of 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 can you identify the y-intercept from the equation y = mx + b?

Back

The y-intercept is the value of b in the equation. It is the value of y when x = 0.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.F.A.3

CCSS.8.EE.B.6

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line falls as it moves from left to right.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 4x - 1?

Back

The slope of the line is 4.

Tags

CCSS.8.EE.B.5

Front

How do you write an equation for a line that starts at 80 and increases by 15 each month?

Back

The equation is y = 15x + 80, where x is the number of months.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the slope of the line represented by the points (1, 2) and (3, 6)?

Back

The slope is (6 - 2) / (3 - 1) = 4 / 2 = 2.

Tags

CCSS.8.EE.B.5